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A226659
Sum_{k=0..n} A000041( binomial(n,k) ), where A000041(n) is the number of partitions of n.
2
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 14 2013
STATUS
approved