cp's OEIS Frontend

A360487 Convolution of A000009 and A000290.

%I A360487 #7 Feb 09 2023 10:45:03
%S A360487 0,1,5,14,31,60,106,176,279,426,631,912,1291,1795,2457,3317,4424,5837,
%T A360487 7626,9875,12684,16171,20476,25764,32228,40094,49626,61131,74966,
%U A360487 91545,111346,134921,162906,196031,235134,281175,335251,398615,472695,559115,659721,776608
%N A360487 Convolution of A000009 and A000290.
%F A360487 a(n) = Sum_{k=0..n} A000009(k) * (n-k)^2.
%F A360487 G.f.: x*(1+x)/(1-x)^3 * Product_{k>=1} (1 + x^k).
%F A360487 a(n) ~ 4 * 3^(5/4) * n^(3/4) * exp(sqrt(n/3)*Pi) / Pi^3.
%p A360487 b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
%p A360487      `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
%p A360487     end:
%p A360487 a:= n-> add(b(n-j)*j^2, j=0..n):
%p A360487 seq(a(n), n=0..42);  # _Alois P. Heinz_, Feb 09 2023
%t A360487 Table[Sum[PartitionsQ[k]*(n-k)^2, {k, 0, n}], {n, 0, 60}]
%t A360487 CoefficientList[Series[x*(1+x)*QPochhammer[-1, x] / (2*(1-x)^3), {x, 0, 60}], x]
%Y A360487 Cf. A000009, A000290, A095944, A360486.
%K A360487 nonn
%O A360487 0,3
%A A360487 _Vaclav Kotesovec_, Feb 09 2023