A293049 Expansion of e.g.f. exp(x^3/(1 - x)).

1, 0, 0, 6, 24, 120, 1080, 10080, 100800, 1149120, 14515200, 199584000, 2973801600, 47740492800, 820928908800, 15049152518400, 292919058432000, 6031865968128000, 130990787582054400, 2991455760887193600, 71659101232502784000, 1796424431562528768000

Offset

0,4

Comments

For n > 4, a(n) is a multiple of 10. - Muniru A Asiru, Oct 09 2017

Links

Seiichi Manyama, Table of n, a(n) for n = 0..444

Formula

E.g.f.: Product_{i>2} exp(x^i).

a(n) ~ n^(n-1/4) * exp(-5/2 + 2*sqrt(n) - n) / sqrt(2). - Vaclav Kotesovec, Sep 30 2017

a(n) = 2*(n-1) * a(n-1) - (n-1)*(n-2) * a(n-2) + 6*binomial(n-1,2) * a(n-3) - 12*binomial(n-1,3) * a(n-4) for n > 3. - Seiichi Manyama, Mar 15 2023

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n-1, j-1)*j!, j=3..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 30 2017
seq(factorial(k)*coeftayl(exp(x^3/(1-x)), x = 0, k), k=0..50); # Muniru A Asiru, Oct 09 2017

Mathematica

CoefficientList[Series[E^(x^3/(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2017 *)

Prog

(PARI) x='x+O('x^66); Vec(serlaplace(exp(x^3/(1-x))))

Crossrefs

Column k=2 of A293053.

E.g.f.: Product_{i>k} exp(x^i): A000262 (k=0), A052845 (k=1), this sequence (k=2), A293050 (k=3).

Sequence in context: A047865 A355285 A182083 * A293123 A355575 A060249

Adjacent sequences: A293046 A293047 A293048 * A293050 A293051 A293052

Keyword

nonn

Author

Seiichi Manyama, Sep 29 2017

Status

approved