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 A378503 #13 Nov 29 2024 08:12:18
%S A378503 1,12,132,1396,14436,147120,1483996,14854968,147821604,1464031120,
%T A378503 14443875984,142042418004,1393053544508,13630170286224,
%U A378503 133092301736232,1297274743175856,12624909478998948,122692158505386960,1190859983017752880,11545524234978791952,111820579340839270416
%N A378503 Expansion of (Sum_{k>=0} binomial(4*k,k) * x^k)^3.
%F A378503 a(n) = Sum_{i+j+k=n, i,j,k >= 0} binomial(4*i,i) * binomial(4*j,j) * binomial(4*k,k).
%F A378503 G.f.: B(x)^3 where B(x) is the g.f. of A005810.
%F A378503 27*a(n) - 256*a(n-1) = 18*A005810(n) - A337291(n) for n > 0.
%o A378503 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, binomial(4*k, k)*x^k)^3)
%Y A378503 Cf. A005810, A078995, A337291, A378484.
%Y A378503 Cf. A002457, A378483.
%K A378503 nonn
%O A378503 0,2
%A A378503 _Seiichi Manyama_, Nov 28 2024