A363509 G.f. satisfies A(x) = exp( Sum_{k>=1} (-1)^(k+1) * (3 + A(x^k)) * x^k/k ).

1, 4, 10, 30, 101, 361, 1354, 5238, 20740, 83683, 342719, 1421019, 5953306, 25162342, 107163924, 459438524, 1981247950, 8588054014, 37398421941, 163534601567, 717776072291, 3161117717887, 13964782042188, 61866495037806, 274792382789958

Offset

0,2

Links

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

Formula

A(x) = Sum_{k>=0} a(k) * x^k = (1+x)^3 * Product_{k>=0} (1+x^(k+1))^a(k).

a(0) = 1; a(n) = (-1/n) * Sum_{k=1..n} ( 3 * (-1)^k + Sum_{d|k} (-1)^(k/d) * d * a(d-1) ) * a(n-k).

Prog

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

Crossrefs

Cf. A004111, A038075, A038076, A363510.

Cf. A363507.

Sequence in context: A114946 A243793 A001551 * A067142 A145453 A346754

Adjacent sequences: A363506 A363507 A363508 * A363510 A363511 A363512

Keyword

nonn

Author

Seiichi Manyama, Jun 06 2023

Status

approved