A362314 a(n) = n! * Sum_{k=0..floor(n/4)} (n/4)^k /(k! * (n-4*k)!).

1, 1, 1, 1, 25, 151, 541, 1471, 84001, 925345, 5682601, 25177681, 2245355641, 35901100951, 312222474565, 1917363070351, 232479594721921, 4873115730725761, 54830346428307601, 430468886732009185, 65997947903313461401, 1711564302775814535511

Offset

0,5

Links

Winston de Greef, Table of n, a(n) for n = 0..431

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

Formula

a(n) = n! * [x^n] exp(x + n*x^4/4).

E.g.f.: exp( ( -LambertW(-x^4) )^(1/4) ) / (1 + LambertW(-x^4)).

From Vaclav Kotesovec, Apr 18 2023: (Start)

a(n) ~ c * n^n / exp(3*n/4), where

c = cosh(1) + cos(1) if mod(n,4)=0,

c = sinh(1) + sin(1) if mod(n,4)=1,

c = cosh(1) - cos(1) if mod(n,4)=2,

c = sinh(1) - sin(1) if mod(n,4)=3. (End)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-x^4))^(1/4))/(1+lambertw(-x^4))))

Crossrefs

Cf. A277614, A362300, A362319.

Sequence in context: A197998 A042214 A215760 * A305687 A147059 A317067

Adjacent sequences: A362311 A362312 A362313 * A362315 A362316 A362317

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2023

Status

approved