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.
%I A377147 #11 Oct 18 2024 10:48:54
%S A377147 1,0,0,3,3,0,6,24,6,10,90,90,25,240,540,261,540,2100,2128,1533,6321,
%T A377147 11236,8064,16884,44173,46980,51156,142939,224991,212400,423426,
%U A377147 882660,1006875,1338558,2991318,4431669,5034296,9457704,17178678,21059737,30809286,59843394,86518266
%N A377147 a(n) = Sum_{k=0..floor(n/3)} binomial(k+2,2) * binomial(k,n-3*k)^2.
%F A377147 G.f.: ((1-x^3-x^4)^2 + 2*x^7) / ((1-x^3-x^4)^2 - 4*x^7)^(5/2).
%o A377147 (PARI) a(n) = sum(k=0, n\3, binomial(k+2, 2)*binomial(k, n-3*k)^2);
%o A377147 (PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
%o A377147 my(N=2, M=50, x='x+O('x^M), X=1-x^3-x^4, Y=7); Vec(sum(k=0, N\2, a089627(N, k)*X^(N-2*k)*x^(Y*k))/(X^2-4*x^Y)^(N+1/2))
%Y A377147 Cf. A377145, A377146.
%Y A377147 Cf. A375470, A376721.
%Y A377147 Cf. A089627.
%K A377147 nonn
%O A377147 0,4
%A A377147 _Seiichi Manyama_, Oct 17 2024