A377527 -id:A377527 - cp's OEIS frontend

A377529 Expansion of e.g.f. 1/(1 - x * exp(x))^2.

1, 2, 10, 66, 560, 5770, 69852, 970886, 15228880, 266006610, 5119447700, 107617719022, 2453167135608, 60268223308826, 1587381621990556, 44619277892537910, 1333135910963656352, 42189279001183102882, 1409741875877923927332, 49597905017847180008126

Offset: 0

Seiichi Manyama, Oct 30 2024

Cf. A006153, A377530.

Cf. A377503, A377527.

With[{nn=20},CoefficientList[Series[1/(1-x Exp[x])^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 04 2025 *)

a(n) = n!*sum(k=0, n, (k+1)*k^(n-k)/(n-k)!);

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

a(n) ~ n! * n/((1 + LambertW(1))^2 * LambertW(1)^n). - Vaclav Kotesovec, Oct 31 2024

A377528 E.g.f. satisfies A(x) = 1/(1 - x * exp(x) * A(x))^4.

Original entry on oeis.org

1, 4, 60, 1548, 58456, 2930020, 183763704, 13866109012, 1224251041248, 123885272536452, 14140672597851880, 1797709847594145364, 251941291752251706576, 38593132701417704324356, 6415647343472197357272984, 1150373241484390263973203540, 221318733487356013660505462464

Offset: 0

Seiichi Manyama, Oct 30 2024

nonn

Cf. A295238, A377503, A377504.

Cf. A377526, A377527.

a(n) = n!*sum(k=0, n, k^(n-k)*binomial(5*k+3, k)/((k+1)*(n-k)!));

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377526.

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(5*k+3,k)/( (k+1)*(n-k)! ).

cp's OEIS Frontend

A377529 Expansion of e.g.f. 1/(1 - x * exp(x))^2.

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