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

0,5

Comments

a(n) = A000041(A007318(n));

T(n,0) = T(n,n) = 1; T(n,1) = T(n,n-1) = A000041(n), n>0.

Links

Indranil Ghosh, Rows 0..20, flattened

Eric Weisstein's World of Mathematics, Partition

Eric Weisstein's World of Mathematics, Binomial Coefficient

Example

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; ...

Mathematica

Flatten[Table[PartitionsP[Binomial[n, k]], {n, 0, 10}, {k, 0, n}]] (* Indranil Ghosh, Feb 21 2017 *)

Prog

(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

Crossrefs

Cf. A226659 (row sums), A128855 (central terms).

Sequence in context: A261365 A261507 A304942 * A061554 A296373 A345710

Adjacent sequences: A090008 A090009 A090010 * A090012 A090013 A090014

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jan 28 2004

Extensions

Data section corrected by Indranil Ghosh, Feb 21 2017

Status

approved