A187667 Coefficient of x^n in (1 + n*x + n*x^2 + n*x^3)^n.

1, 1, 8, 90, 1312, 23625, 505116, 12475596, 348942336, 10888165395, 374606200000, 14077548113398, 573396296212224, 25150850370412156, 1181513742628738624, 59165118490203450000, 3145241884988171878400, 176865209305943158023799, 10486960289673977419520256

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*trinomial(k,n-k)*n^k.

Maple

A027907 := proc(n, k) add( binomial(n, j)*binomial(n-j, k-2*j), j=0..n) ; end proc:
A187667 := proc(n) add( binomial(n, k)*A027907(k, n-k)*n^k, k=0..n) ; end proc:
seq(A187667(n), n=0..10) ; # R. J. Mathar, Mar 27 2011

Mathematica

a[n_] := If[n == 0, 1, Coefficient[(1 + n x + n x^2 + n x^3)^n, x^n]]
Table[a[n], {n, 0, 12}]

Prog

(Maxima) makelist(coeff(expand((1+n*x+n*x^2+n*x^3)^n), x, n), n, 0, 12);

Crossrefs

Cf. A092366, A027907.

Sequence in context: A056784 A166769 A323960 * A331512 A092956 A345876

Adjacent sequences: A187664 A187665 A187666 * A187668 A187669 A187670

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved