A362491 E.g.f. satisfies A(x) = exp(x + x^4/4 * A(x)^4).

1, 1, 1, 1, 7, 151, 2251, 26251, 273841, 3281041, 61021801, 1518719401, 38199828151, 905801252071, 21398411003971, 560160675014851, 17260034904184801, 596005144436100001, 21359751419836426321, 773082506262449261521, 28839945213850125032551

Offset

0,5

Links

Table of n, a(n) for n=0..20.

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

Formula

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

a(n) = n! * Sum_{k=0..floor(n/4)} (1/4)^k * (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).

Prog

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

Crossrefs

Cf. A362474, A362478.

Cf. A362473, A362494.

Sequence in context: A364845 A339582 A232446 * A202558 A159659 A100868

Adjacent sequences: A362488 A362489 A362490 * A362492 A362493 A362494

Keyword

nonn

Author

Seiichi Manyama, Apr 22 2023

Status

approved