A032307 Shifts left 2 places under "EFK" (unordered, size, unlabeled) transform.

1, 1, 1, 1, 2, 2, 4, 6, 10, 17, 29, 50, 88, 156, 279, 498, 909, 1639, 3010, 5495, 10152, 18674, 34745, 64312, 120197, 223850, 420057, 785683, 1480429, 2779462, 5253203, 9899964, 18761327, 35461501, 67383407, 127689713

Offset: 1

Author

Christian G. Bower

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A032305.

Programs

PARI

EFK(p,n)={prod(k=1, n, 1 + polcoef(p,k)*x^k + O(x*x^n))}
seq(n)={my(p=O(1));for(i=0, (n-1)\2, p=1+x*EFK(x*p, 2*i)); Vec(p+O(x^n))} \\ Andrew Howroyd, Sep 20 2018

Formula

G.f.: x + x^2 * exp(Sum_{n>=1} Sum_{k>=1} (-1)^(k+1) * a(n)^k * x^(n*k) / k). - Ilya Gutkovskiy, Jun 30 2021