A363405 G.f. satisfies A(x) = exp( Sum_{k>=1} (A(x^k) + A(i*x^k) + A(-x^k) + A(i^3*x^k))/4 * x^k/k ), where i = sqrt(-1).

1, 1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 5, 5, 10, 12, 13, 13, 26, 34, 36, 37, 74, 97, 105, 107, 215, 293, 320, 328, 658, 905, 998, 1025, 2058, 2878, 3194, 3292, 6611, 9316, 10412, 10748, 21594, 30697, 34470, 35663, 71668, 102446, 115575, 119761, 240740, 345940, 391726, 406571, 817453, 1179322, 1339851

Offset

0,6

Links

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

Formula

A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(4*k+1))^a(4*k).

A(x) * A(i*x) * A(-x) * A(i^3*x) = A(x^4).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 4} d * a(d-1) ) * a(n-k).

Prog

(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, sum(m=0, 3, subst(A, x, I^m*x^k))/4*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A195865, A363404.

Cf. A363337.

Sequence in context: A078635 A286305 A046768 * A274151 A216393 A045812

Adjacent sequences: A363402 A363403 A363404 * A363406 A363407 A363408

Keyword

nonn

Author

Seiichi Manyama, May 31 2023

Status

approved