A363581 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + 3*x^k)) ).

1, 1, -1, 4, -6, 11, -22, 62, -151, 353, -867, 2261, -5861, 15178, -39878, 106099, -283823, 763248, -2065453, 5621318, -15368682, 42190539, -116281176, 321647511, -892617214, 2484583934, -6935203356, 19408586888, -54447145335, 153084848495

Offset

0,4

Links

Table of n, a(n) for n=0..29.

Formula

A(x) = (1 + 3*x) * B(x) where B(x) is the g.f. of A363579.

a(n) = A363579(n) + 3*A363579(n-1) for n > 0.

Prog

(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*x^k/(k*(1+3*x^k)))+x*O(x^n))); Vec(A);

Crossrefs

Cf. A052855, A198518, A363545, A363546, A363580.

Cf. A363579.

Sequence in context: A302428 A336142 A091280 * A219520 A336343 A330459

Adjacent sequences: A363578 A363579 A363580 * A363582 A363583 A363584

Keyword

sign

Author

Seiichi Manyama, Jun 10 2023

Status

approved