A356796 E.g.f. satisfies A(x) = 1/(1 - x)^(x * A(x)^3).

1, 0, 2, 3, 92, 450, 14454, 141540, 4980128, 78711696, 3048567480, 68677353360, 2930551701384, 86832573553440, 4079649847428960, 150444517302424800, 7768028697749806080, 342721736137376184960, 19392702029822685015360, 994397473912386435004800

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (3*k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!.

E.g.f.: A(x) = Sum_{k>=0} (3*k+1)^(k-1) * (-x * log(1-x))^k / k!.

E.g.f.: A(x) = exp( -LambertW(3 * x * log(1-x))/3 ).

E.g.f.: A(x) = ( LambertW(3 * x * log(1-x))/(3 * x * log(1-x)) )^(1/3).

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k+1)^(k-1)*(-x*log(1-x))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(3*x*log(1-x))/3)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(3*x*log(1-x))/(3*x*log(1-x)))^(1/3)))

Crossrefs

Cf. A066166, A355842, A356795.

Cf. A356787.

Sequence in context: A224934 A299691 A042901 * A356786 A002983 A118167

Adjacent sequences: A356793 A356794 A356795 * A356797 A356798 A356799

Keyword

nonn

Author

Seiichi Manyama, Aug 28 2022

Status

approved