A362323 -id:A362323 - cp's OEIS frontend

A362321 a(n) = n! * Sum_{k=0..floor(n/4)} n^k /(k! * (n-4*k)!).

1, 1, 1, 1, 97, 601, 2161, 5881, 1303681, 14723857, 90770401, 402581521, 139389608161, 2284512533161, 19946635524817, 122623661651401, 57728368477678081, 1240234284406887841, 14010634784751445441, 110117252571345122977

Offset: 0

Seiichi Manyama, Apr 16 2023

nonn

Winston de Greef, Table of n, a(n) for n = 0..408
Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A362301, A362323.

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-4*x^4)/4)^(1/4))/(1+lambertw(-4*x^4))))

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

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

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

A362321 a(n) = n! * Sum_{k=0..floor(n/4)} n^k /(k! * (n-4*k)!).

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