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A007121 E.g.f. ( (1+x)^x )^x.
(Formerly M4099)
1
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

Table of n, a(n) for n=0..23.

FORMULA

a(n)= n!*Sum_{k=0..n/2} Stirling1(n-2*k,k)/(n-2*k)!. - Vladimir Kruchinin, Dec 13 2011

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/2); /* Vladimir Kruchinin, Dec 13 2011 */

CROSSREFS

Sequence in context: A128453 A185616 A052747 * A152786 A267309 A206039

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 January 16 03:30 EST 2019. Contains 319184 sequences. (Running on oeis4.)