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 A377146 #10 Oct 18 2024 10:49:02
%S A377146 1,0,3,3,6,24,16,90,105,250,561,765,2143,3108,6861,12985,22221,47988,
%T A377146 79463,161451,293610,535836,1042188,1835898,3534766,6399198,11805756,
%U A377146 22021232,39718497,74193924,134489713,247165839,453235266,822748406,1512078192,2741606052
%N A377146 a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,2) * binomial(k,n-2*k)^2.
%F A377146 G.f.: ((1-x^2-x^3)^2 + 2*x^5) / ((1-x^2-x^3)^2 - 4*x^5)^(5/2).
%o A377146 (PARI) a(n) = sum(k=0, n\2, binomial(k+2, 2)*binomial(k, n-2*k)^2);
%o A377146 (PARI) a089627(n, k) = n!/((n-2*k)!*k!^2);
%o A377146 my(N=2, M=40, x='x+O('x^M), X=1-x^2-x^3, Y=5); 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 A377146 Cf. A377145, A377147.
%Y A377146 Cf. A298567, A375218.
%Y A377146 Cf. A089627.
%K A377146 nonn
%O A377146 0,3
%A A377146 _Seiichi Manyama_, Oct 17 2024