A362317 -id:A362317 - cp's OEIS frontend

A362352 a(n) = n! * Sum_{k=0..floor(n/4)} (k/24)^k / (k! * (n-4*k)!).

1, 1, 1, 1, 2, 6, 16, 36, 211, 1387, 6511, 23431, 225721, 2207921, 14610597, 71848141, 958259121, 12403693681, 105819536881, 659686502257, 11235532306021, 180826378073461, 1888306425160541, 14256573124903341, 295428115205647117, 5683724892725141901

Offset: 0

Seiichi Manyama, Apr 17 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..494
Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A362350, A362351.

Cf. A362317.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^4/24))))

E.g.f.: exp(x) / (1 + LambertW(-x^4/24)).

a(n) ~ (exp(2^(3/4)*3^(1/4)*exp(-1/4)) + (-1)^n/exp(2^(3/4)*3^(1/4)*exp(-1/4)) + 2*cos(2^(3/4)*3^(1/4)*exp(-1/4) - Pi*n/2)) * n^n / (2^(3*n/4 + 1) * 3^(n/4) * exp(3*n/4)). - Vaclav Kotesovec, Apr 18 2023

A362336 a(n) = n! * Sum_{k=0..floor(n/5)} (n/120)^k /(k! * (n-5*k)!).

Original entry on oeis.org

1, 1, 1, 1, 1, 6, 37, 148, 449, 1135, 15121, 172789, 1207009, 6106816, 24748725, 510855346, 8524169473, 84981641837, 602009065729, 3357322881625, 93871272204481, 2059974308136466, 26683062726210661, 243032907824598816, 1725747644222610625

Offset: 0

Seiichi Manyama, Apr 16 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..484
Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A362173, A362317.

Cf. A275423, A362319, A362323.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-24*lambertw(-x^5/24))^(1/5))/(1+lambertw(-x^5/24))))

a(n) = n! * [x^n] exp(x + n*x^5/120).

E.g.f.: exp( ( -24*LambertW(-x^5/24) )^(1/5) ) / (1 + LambertW(-x^5/24)).

cp's OEIS Frontend

A362352 a(n) = n! * Sum_{k=0..floor(n/4)} (k/24)^k / (k! * (n-4*k)!).

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