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%I #9 Feb 01 2019 19:58:45
%S 1,1,8,90,1312,23625,505116,12475596,348942336,10888165395,
%T 374606200000,14077548113398,573396296212224,25150850370412156,
%U 1181513742628738624,59165118490203450000,3145241884988171878400,176865209305943158023799,10486960289673977419520256
%N Coefficient of x^n in (1 + n*x + n*x^2 + n*x^3)^n.
%F a(n) = Sum_{k=0..n} binomial(n,k)*trinomial(k,n-k)*n^k.
%p A027907 := proc(n,k) add( binomial(n,j)*binomial(n-j,k-2*j),j=0..n) ; end proc:
%p A187667 := proc(n) add( binomial(n,k)*A027907(k,n-k)*n^k,k=0..n) ; end proc:
%p seq(A187667(n),n=0..10) ; # _R. J. Mathar_, Mar 27 2011
%t a[n_] := If[n == 0, 1, Coefficient[(1 + n x + n x^2 + n x^3)^n, x^n]]
%t Table[a[n], {n, 0, 12}]
%o (Maxima) makelist(coeff(expand((1+n*x+n*x^2+n*x^3)^n),x,n),n,0,12);
%Y Cf. A092366, A027907.
%K nonn,easy
%O 0,3
%A _Emanuele Munarini_, Mar 12 2011