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A290690 E.g.f.: exp(Sum_{k>=1} (k-1)^3*x^k). 2
1, 0, 2, 48, 660, 8640, 132600, 2520000, 56046480, 1375557120, 36456769440, 1041522451200, 32083867126080, 1061964845061120, 37543201808112000, 1409292653408640000, 55917035430800544000, 2337184142686903910400, 102624865930477758067200 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified May 11 16:48 EDT 2021. Contains 343805 sequences. (Running on oeis4.)