A363337 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^(4*k)) * x^k/k ).

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 10, 11, 12, 14, 16, 18, 19, 22, 26, 29, 31, 34, 40, 45, 48, 52, 60, 68, 74, 80, 90, 102, 111, 121, 136, 152, 166, 180, 201, 225, 245, 264, 294, 329, 360, 387, 426, 476, 521, 562, 615, 683, 750, 809, 883, 978, 1071, 1156, 1259, 1389, 1523

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(k).

A(x) * A(i*x) * A(-x) * A(i^3*x) = A(x^4), where i=sqrt(-1).

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

Prog

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

Crossrefs

Cf. A000081, A115593, A363336.

Sequence in context: A199119 A321423 A035451 * A304633 A124746 A124789

Adjacent sequences: A363334 A363335 A363336 * A363338 A363339 A363340

Keyword

nonn

Author

Seiichi Manyama, May 28 2023

Status

approved