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PeterBurbery`Combinatorics`
ModifiedCentralBinomialCoefficient  |
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Details and Options
Examples
(3)
Basic Examples
(1)
A table of values.
In[1]:=
 | ModifiedCentralBinomialCoefficient |
Out[1]=
{1,2,3,6,10,20,35,70,126,252,462,924,1716,3432,6435,12870,24310,48620,92378,184756,352716,705432,1352078,2704156,5200300,10400600,20058300,40116600,77558760,155117520,300540195,601080390,1166803110,2333606220,4537567650,9075135300,17672631900,35345263800,68923264410,137846528820}
Put spaces between the numbers for sequences@oeis.
In[2]:=
StringRiffle
[Range[40]]," "
 | ModifiedCentralBinomialCoefficient |
Out[2]=
1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 1352078 2704156 5200300 10400600 20058300 40116600 77558760 155117520 300540195 601080390 1166803110 2333606220 4537567650 9075135300 17672631900 35345263800 68923264410 137846528820
Add lookup in front.
In[3]:=
StringJoin"lookup ",StringRiffle
[Range[40]]," "
 | ModifiedCentralBinomialCoefficient |
Out[3]=
lookup 1 2 3 6 10 20 35 70 126 252 462 924 1716 3432 6435 12870 24310 48620 92378 184756 352716 705432 1352078 2704156 5200300 10400600 20058300 40116600 77558760 155117520 300540195 601080390 1166803110 2333606220 4537567650 9075135300 17672631900 35345263800 68923264410 137846528820
You can copy this to the clipboard.
In[4]:=
CopyToClipboardStringJoin"lookup ",StringRiffle
[Range[40]]," "
 | ModifiedCentralBinomialCoefficient |
Send what is copied with no subject to sequences@oeis.org to do an email lookup.
Here's a dataset.
In[5]:=
DatasetAssociationMap
[Range[40]]
| ModifiedCentralBinomialCoefficient |
Out[5]=
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Ask for a discrete asymptotic.
In[6]:=
DiscreteAsymptotic
[n],n∞
| ModifiedCentralBinomialCoefficient |
Out[6]=
1
Beta[Quotient[n,2],1+n-Quotient[n,2]]Quotient[n,2]
In[7]:=
1
Quotient[n,2]Β(Quotient[n,2],n-Quotient[n,2]+1)
Compute this for a big number.
In[8]:=
n[1000]
1
Quotient[n,2]Β(Quotient[n,2],n-Quotient[n,2]+1)
Out[8]=
270288240945436569515614693625975275496152008446548287007392875106625428705522193898612483924502370165362606085021546104802209750050679917549894219699518475423665484263751733356162464079737887344364574161119497604571044985756287880514600994219426752366915856603136862602484428109296905863799821216320
Is this the same?
In[9]:=
 | ModifiedCentralBinomialCoefficient |
1
Quotient[n,2]Β(Quotient[n,2],n-Quotient[n,2]+1)
Out[9]=
True
Properties & Relations
(1)
Possible Issues
(1)
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