A363470 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} A(-x^k) * x^k/k ).

1, 2, -1, -6, 7, 42, -58, -366, 513, 3406, -4846, -33310, 48304, 339446, -499133, -3565468, 5294439, 38312242, -57332347, -419177900, 631252549, 4654229300, -7045498256, -52310262192, 79531957334, 593986308994, -906439292326, -6803984285256

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

A(x) = B(x)^2 where B(x) is the g.f. of A200438.

A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(k+1))^(2 * (-1)^k * a(k)).

a(0) = 1; a(n) = (2/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-1)^(d-1) * a(d-1) ) * a(n-k).

Prog

(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(2*sum(k=1, i, subst(A, x, -x^k)*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A000151, A200438, A363471.

Sequence in context: A192232 A358723 A243320 * A319897 A350009 A350010

Adjacent sequences: A363467 A363468 A363469 * A363471 A363472 A363473

Keyword

sign

Author

Seiichi Manyama, Jun 03 2023

Status

approved