OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..200
FORMULA
From Seiichi Manyama, Jul 09 2022: (Start)
a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * Stirling2(n-2*k,k)/(n-2*k)!.
a(0) = 1; a(n) = -(n-1)! * Sum_{k=3..n} k/(k-2)! * a(n-k)/(n-k)!. (End)
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Exp[x^2 (1-Exp[x])], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jul 16 2021 *)
PROG
(PARI) x='x+O('x^66); Vec(serlaplace(exp(x^2*(1-exp(x)))))
(PARI) a(n) = n!*sum(k=0, n\3, (-1)^k*stirling(n-2*k, k, 2)/(n-2*k)!); \\ Seiichi Manyama, Jul 09 2022
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-(i-1)!*sum(j=3, i, j/(j-2)!*v[i-j+1]/(i-j)!)); v; \\ Seiichi Manyama, Jul 09 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 27 2017
STATUS
approved