A156733 Euler transform of n*A065958(n).

1, 1, 11, 41, 176, 606, 2391, 8091, 28636, 95056, 316048, 1014240, 3237325, 10082015, 31109500, 94352346, 283209381, 838650191, 2458835711, 7127912979, 20471486368, 58224189612, 164181018330, 458982667630, 1273039111210, 3503609456548, 9572771822745, 25971150308985

Offset: 0

Author

Paul D. Hanna and Vladeta Jovovic, Feb 14 2009

Keywords

• nonn

Comments

Compare to the g.f. of planar partitions (A000219): exp( Sum_{n>=1} sigma(n,2)*x^n/n ) = Product_{n>=1} 1/(1-x^n)^n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A001157, A156303, A065827, A301978, A301980.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*numtheory[sigma][2](j^2), j=1..n)/n)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Sep 24 2016

Mathematica

a[0] = 1;
a[n_] := a[n] = (1/n) Sum[DivisorSigma[2, k^2] a[n-k], {k, 1, n}];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 03 2020 *)

PARI

{a(n)=polcoeff(exp(sum(m=1,n,sigma(m^2,2)*x^m/m)+x*O(x^n)),n)}
for(n=0,21,print1(a(n),", "))

Formula

a(n) = (1/n)*Sum_{k=1..n} sigma_2(k^2)*a(n-k) for n>0, with a(0) = 1.

G.f.: exp( Sum_{n>=1} A065827(n)*x^n/n ), where A065827(n) = sigma_2(n^2) is the sum of squares of the divisors of n^2. - Paul D. Hanna, Aug 09 2012