A372183 E.g.f. A(x) satisfies A(x) = exp( x * A(x)^5 / (1 - x * A(x)^2) ).

1, 1, 13, 340, 13713, 752516, 52372051, 4421017602, 438996446545, 50142716621848, 6477138263806011, 933667525669154486, 148582199464010331289, 25874197258988478298068, 4894174597530612144797299, 999256176035969437218129946, 219035687330062179838536993441

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.

Prog

(PARI) a(n, r=1, s=1, t=5, u=2) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);

Crossrefs

Cf. A212722, A361093, A365012.

Cf. A372165.

Sequence in context: A238652 A041315 A041312 * A096717 A296679 A125119

Adjacent sequences: A372180 A372181 A372182 * A372184 A372185 A372186

Keyword

nonn

Author

Seiichi Manyama, Apr 21 2024

Status

approved