cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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