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 A377145 #19 Oct 18 2024 10:49:08
%S A377145 1,3,9,34,111,351,1103,3384,10224,30536,90222,264186,767663,2215623,
%T A377145 6356907,18143300,51540885,145801395,410888595,1153964520,3230723826,
%U A377145 9019081038,25112021154,69750583164,193303849531,534602071341,1475644537323,4065845732794
%N A377145 a(n) = Sum_{k=0..n} binomial(k+2,2) * binomial(k,n-k)^2.
%F A377145 G.f.: ((1-x-x^2)^2 + 2*x^3) / ((1-x-x^2)^2 - 4*x^3)^(5/2).
%o A377145 (PARI) a(n) = sum(k=0, n, binomial(k+2, 2)*binomial(k, n-k)^2);
%o A377145 (PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
%o A377145 my(N=2, M=30, x='x+O('x^M), X=1-x-x^2, Y=3); 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 A377145 Cf. A051286, A182884, A377148, A377152, A377153, A377158, A377159.
%Y A377145 Cf. A377146, A377147.
%Y A377145 Cf. A089627.
%K A377145 nonn
%O A377145 0,2
%A A377145 _Seiichi Manyama_, Oct 17 2024