cp's OEIS Frontend

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

%I A226659 #10 Feb 21 2017 10:44:53
%S A226659 1,2,4,8,23,100,1003,31382,5149096,7091568720,287786595280763,
%T A226659 539018517346414192796,1130813038175196801809538188145,
%U A226659 2336855300714703790840987155549462486654700,7636154577344556445476348286247799105605643795614728449082014
%N A226659 Sum_{k=0..n} A000041( binomial(n,k) ), where A000041(n) is the number of partitions of n.
%C A226659 Compare to the number of partitions of 2^n (A068413).
%H A226659 Indranil Ghosh, <a href="/A226659/b226659.txt">Table of n, a(n) for n = 0..20</a>
%F A226659 Row sums of triangle A090011.
%e A226659 Equals the row sums of triangle A090011, which begins:
%e A226659 1;
%e A226659 1, 1;
%e A226659 1, 2, 1;
%e A226659 1, 3, 3, 1;
%e A226659 1, 5, 11, 5, 1;
%e A226659 1, 7, 42, 42, 7, 1;
%e A226659 1, 11, 176, 627, 176, 11, 1;
%e A226659 1, 15, 792, 14883, 14883, 792, 15, 1;
%e A226659 1, 22, 3718, 526823, 4087968, 526823, 3718, 22, 1; ...
%t A226659 Table[Sum[PartitionsP[Binomial[n,k]],{k,0,n}],{n,0,20}] (* _Indranil Ghosh_, Feb 21 2017 *)
%o A226659 (PARI) {a(n)=sum(k=0,n,numbpart(binomial(n,k)))}
%o A226659 for(n=0,15,print1(a(n),", "))
%Y A226659 Cf. A090011, A068413, A128855, A000041.
%K A226659 nonn
%O A226659 0,2
%A A226659 _Paul D. Hanna_, Jun 14 2013