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A191422
Expansion of e.g.f. (1 + x + x^2)^x.
2
1, 0, 2, 3, -4, 90, -126, -840, 21104, -137592, -88920, 15741000, -197234808, 535289040, 25582565904, -522317151720, 3223601137920, 75590725210560, -2388641226278976, 23718732310200960, 361277667059425920, -17515819241263405440, 246424647059545933440
OFFSET
0,3
LINKS
FORMULA
E.g.f.: (1 + x + x^2)^x.
a(n) = n!*Sum_{m=1..n} Sum_{k=0..n-2*m} Stirling1(m+k, m)*binomial(m+k, n-2*m-k)/(m+k)! for n > 0, a(0)=1.
MAPLE
S:= series((1+x+x^2)^x, x, 41):
seq(coeff(S, x, k)*k!, k=0..40); # Robert Israel, Apr 28 2021
PROG
(Maxima)
a(n):=if n=0 then 1 else (sum(sum((stirling1(m+k, m)*binomial(m+k, n-2*m-k))/(m+k)!, k, 0, n-2*m), m, 1, n))*n!;
(PARI) my(x='x+O('x^30)); Vec(serlaplace((1+x+x^2)^x)) \\ Michel Marcus, Apr 28 2021
CROSSREFS
Sequence in context: A037395 A009496 A263281 * A008405 A037431 A262526
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Jun 02 2011
STATUS
approved