A377527 E.g.f. satisfies A(x) = 1/(1 - x * exp(x) * A(x)^2)^2.

1, 2, 26, 618, 22256, 1081770, 66401532, 4931389358, 430108545680, 43104305664594, 4881518010253460, 616559703960596022, 85935621525038617752, 13102417265843584412474, 2169337115977056447577820, 387609934848899388554651550, 74340899731294447790784890912

Offset

0,2

Links

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377526.

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(5*k+1,k)/( (2*k+1)*(n-k)! ).

a(n) ~ 5^(3/2) * sqrt(1 + LambertW(256/3125)) * n^(n-1) / (16 * exp(n) * LambertW(256/3125)^n). - Vaclav Kotesovec, Feb 04 2026

Mathematica

Join[{1}, Table[n! * Sum[k^(n-k) * Binomial[5*k+1, k] / ((2*k+1)*(n-k)!), {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Feb 04 2026 *)

Prog

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

Crossrefs

Cf. A377526, A377528.

Cf. A377503, A377529.

Sequence in context: A255538 A387430 A302719 * A377547 A384495 A377632

Adjacent sequences: A377524 A377525 A377526 * A377528 A377529 A377530

Keyword

nonn

Author

Seiichi Manyama, Oct 30 2024

Status

approved