A226659 Sum_{k=0..n} A000041( binomial(n,k) ), where A000041(n) is the number of partitions of n.

1, 2, 4, 8, 23, 100, 1003, 31382, 5149096, 7091568720, 287786595280763, 539018517346414192796, 1130813038175196801809538188145, 2336855300714703790840987155549462486654700, 7636154577344556445476348286247799105605643795614728449082014

Offset

0,2

Comments

Compare to the number of partitions of 2^n (A068413).

Links

Indranil Ghosh, Table of n, a(n) for n = 0..20

Formula

Row sums of triangle A090011.

Example

Equals the row sums of triangle A090011, which 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; ...

Mathematica

Table[Sum[PartitionsP[Binomial[n, k]], {k, 0, n}], {n, 0, 20}] (* Indranil Ghosh, Feb 21 2017 *)

Prog

(PARI) {a(n)=sum(k=0, n, numbpart(binomial(n, k)))}
for(n=0, 15, print1(a(n), ", "))

Crossrefs

Cf. A090011, A068413, A128855, A000041.

Sequence in context: A295419 A290816 A181070 * A009327 A027168 A078751

Adjacent sequences: A226656 A226657 A226658 * A226660 A226661 A226662

Keyword

nonn

Author

Paul D. Hanna, Jun 14 2013

Status

approved