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A293049
Expansion of e.g.f. exp(x^3/(1 - x)).
7
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
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
From Seiichi Manyama, Jun 17 2024: (Start)
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-2*k-1,n-3*k)/k!.
a(0) = 1; a(n) = (n-1)! * Sum_{k=3..n} k * a(n-k)/(n-k)!. (End)
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 29 2017
STATUS
approved