A191422 Expansion of e.g.f. (1 + x + x^2)^x.

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

Robert Israel, Table of n, a(n) for n = 0..448

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

Adjacent sequences: A191419 A191420 A191421 * A191423 A191424 A191425

Keyword

sign

Author

Vladimir Kruchinin, Jun 02 2011

Status

approved