A090011 T(n,k) = number of partitions of binomial(n,k), 0<=k<=n, triangular array read by rows.
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 11, 5, 1, 1, 7, 42, 42, 7, 1, 1, 11, 176, 627, 176, 11, 1, 1, 15, 792, 14883, 14883, 792, 15, 1, 1, 22, 3718, 526823, 4087968, 526823, 3718, 22, 1, 1, 30, 17977, 26543660, 3519222692, 3519222692, 26543660, 17977, 30, 1, 1, 42, 89134
Offset: 0
Examples
Triangle begins: 1; 1, 1; 1, 2, 1; 1, 3, 3, 1; 1, 5, 11, 5, 1; 1, 7, 42, 42, 7, 1; 1, 11, 176, 627, 176, 11, 1; 1, 15, 792, 14883, 14883, 792, 15, 1; 1, 22, 3718, 526823, 4087968, 526823, 3718, 22, 1; 1, 30, 17977, 26543660, 3519222692, 3519222692, 26543660, 17977, 30, 1; 1, 42, 89134, 1844349560, 9275102575355, 269232701252579, 9275102575355, 1844349560, 89134, 42, 1; ...
Links
- Indranil Ghosh, Rows 0..20, flattened
- Eric Weisstein's World of Mathematics, Partition
- Eric Weisstein's World of Mathematics, Binomial Coefficient
Programs
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Mathematica
Flatten[Table[PartitionsP[Binomial[n,k]],{n,0,10},{k,0,n}]] (* Indranil Ghosh, Feb 21 2017 *) -
PARI
T(n,k)=numbpart(binomial(n,k)) for(n=0,10,for(k=0,n,print1(T(n,k),", "));print()) \\ Paul D. Hanna, Jun 14 2013
Extensions
Data section corrected by Indranil Ghosh, Feb 21 2017
Comments