A362320 -id:A362320 - cp's OEIS frontend

A362315 a(n) = n! * Sum_{k=0..floor(n/4)} (-n/4)^k /(k! * (n-4*k)!).

1, 1, 1, 1, -23, -149, -539, -1469, 77281, 911737, 5657401, 25134121, -2065730039, -35352993389, -310739232803, -1913714425349, 213881558916481, 4797269708789041, 54560246286936241, 429606655679843857, -60718212515535701399, -1684610587476711352709

Offset: 0

Seiichi Manyama, Apr 15 2023

sign

Winston de Greef, Table of n, a(n) for n = 0..431
Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A362276, A362304, A362320.

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

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

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

A362324 a(n) = n! * Sum_{k=0..floor(n/5)} (-n)^k / (k! * (n-5*k)!).

Original entry on oeis.org

1, 1, 1, 1, 1, -599, -4319, -17639, -53759, -136079, 181137601, 2414356561, 17242917121, 87695201881, 355974659041, -734340892685399, -14279571631503359, -145614163414530719, -1037158816523518079, -5794132157196668639, 16192314610730781350401

Offset: 0

Seiichi Manyama, Apr 16 2023

sign

Seiichi Manyama, Table of n, a(n) for n = 0..414
Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A362282, A362305, A362322.

Cf. A351906, A362320.

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

a(n) = n! * [x^n] exp(x - n*x^5).

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

cp's OEIS Frontend

A362315 a(n) = n! * Sum_{k=0..floor(n/4)} (-n/4)^k /(k! * (n-4*k)!).

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