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

Author

Reinhard Zumkeller, Jan 28 2004

Keywords

• nonn
• tabl

Comments

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

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

Crossrefs

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

Programs

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