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 A378484 #22 Jul 19 2025 12:12:58
%S A378484 1,16,208,2480,28176,310336,3344688,35472672,371570320,3853862080,
%T A378484 39650662720,405221752112,4117879215472,41643345090240,
%U A378484 419362920305952,4207604570770752,42079232716865424,419609034657373120,4173470598366784960,41413032430984848832,410071444666659404352
%N A378484 Expansion of (Sum_{k>=0} binomial(4*k,k) * x^k)^4.
%H A378484 Seiichi Manyama, <a href="/A378484/b378484.txt">Table of n, a(n) for n = 0..1000</a>
%F A378484 a(n) = Sum_{i+j+k+l=n, i,j,k,l >= 0} binomial(4*i,i) * binomial(4*j,j) * binomial(4*k,k) * binomial(4*l,l).
%F A378484 G.f.: B(x)^4 where B(x) is the g.f. of A005810.
%F A378484 27*a(n) - 256*a(n-1) = 18*A078995(n) + 8*A005810(n) for n > 0.
%F A378484 a(n) ~ n * 2^(8*n + 2) / 3^(3*n + 2) * (1 + 2^(7/2)/(3^(3/2)*sqrt(Pi*n))). - _Vaclav Kotesovec_, Jul 19 2025
%t A378484 nmax = 20; CoefficientList[Series[Sum[Binomial[4*k,k] * x^k, {k, 0, nmax}]^4, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 19 2025 *)
%o A378484 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, binomial(4*k, k)*x^k)^4)
%Y A378484 Cf. A000302, A378483.
%Y A378484 Cf. A005810, A078995.
%K A378484 nonn
%O A378484 0,2
%A A378484 _Seiichi Manyama_, Nov 28 2024