OFFSET
0,4
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..452
FORMULA
a(n) = n!*Sum_{k=0..floor(n/3)} Stirling1(n-2*k,k)/(n-2*k)!. - Vladimir Kruchinin, Dec 13 2011
a(0) = 1; a(n) = -(n-1)! * Sum_{k=3..n} (-1)^k * k/(k-2) * a(n-k)/(n-k)!. - Seiichi Manyama, Jul 09 2022
MAPLE
A007121 := proc(n)
n!*coeftayl( (1+x)^(x^2), x=0, n) ;
end proc:
seq(A007121(n), n=0..40) ; # R. J. Mathar, Dec 15 2011
MATHEMATICA
With[{nn=30}, CoefficientList[Series[((1+x)^x)^x, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 24 2014 *)
PROG
(Maxima)
a(n):=n!*sum(stirling1(n-2*k, k)/(n-2*k)!, k, 0, n/3); /* Vladimir Kruchinin, Dec 13 2011 */
(PARI) a(n) = n!*sum(k=0, n\3, stirling(n-2*k, k, 1)/(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, (-1)^j*j/(j-2)*v[i-j+1]/(i-j)!)); v; \\ Seiichi Manyama, Jul 09 2022
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Signs added by R. J. Mathar and Vladimir Kruchinin, Dec 15 2011
STATUS
approved
