A290690 E.g.f.: exp(Sum_{k>=1} (k-1)^3*x^k).

1, 0, 2, 48, 660, 8640, 132600, 2520000, 56046480, 1375557120, 36456769440, 1041522451200, 32083867126080, 1061964845061120, 37543201808112000, 1409292653408640000, 55917035430800544000, 2337184142686903910400, 102624865930477758067200

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..407

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} (k-1)^3*k*a(n-k)/(n-k)! for n > 0.

From Vaclav Kotesovec, Jul 31 2021: (Start)

E.g.f.: exp(x^2*(1 + 4*x + x^2)/(1-x)^4).

a(n) ~ exp(65/384 - 101 * 2^(2/5) * 3^(4/5) * n^(1/5) / 1200 + 11 * 2^(4/5) * 3^(3/5) * n^(2/5) / 80 - 2^(-4/5) * 3^(2/5) * n^(3/5) + 5 * 2^(-7/5) * 3^(1/5) * n^(4/5) - n) * 2^(3/10) * 3^(1/10) * n^(n - 1/10) / sqrt(5).

(End)

Mathematica

nmax = 20; CoefficientList[Series[Exp[x^2*(1 + 4*x + x^2)/(1-x)^4], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 31 2021 *)

Prog

(PARI) {a(n) = n!*polcoeff(exp(sum(k=1, n, (k-1)^3*x^k)+x*O(x^n)), n)}

Crossrefs

E.g.f.: exp(Sum_{k>=1} (k-1)^m*x^k): A000262 (m=0), A052887 (m=1), A288270 (m=2), this sequence (m=3).

Cf. A255819.

Sequence in context: A005429 A035606 A157057 * A013523 A260846 A009670

Adjacent sequences: A290687 A290688 A290689 * A290691 A290692 A290693

Keyword

nonn

Author

Seiichi Manyama, Oct 20 2017

Status

approved