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A007121 Expansion of e.g.f. ( (1+x)^x )^x.
(Formerly M4099)
4
1, 0, 0, 6, -12, 40, 180, -1512, 11760, -38880, 20160, 2106720, -22381920, 173197440, -703999296, -1737489600, 86030380800, -1149696737280, 11455162974720, -89560399541760, 636617260339200, -6318191386644480, 139398889956480000, -3797936822885990400 (list; graph; refs; listen; history; text; internal format)
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):=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

Cf. A240989.

Sequence in context: A185616 A307181 A052747 * A356910 A353228 A351503

Adjacent sequences:  A007118 A007119 A007120 * A007122 A007123 A007124

KEYWORD

sign

AUTHOR

Simon Plouffe

EXTENSIONS

Signs added by R. J. Mathar, Vladimir Kruchinin, Dec 15 2011

STATUS

approved

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Last modified October 7 09:17 EDT 2022. Contains 357270 sequences. (Running on oeis4.)