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 A382874 #18 Apr 08 2025 13:59:50
%S A382874 1,42,1890,32340,378378,3567564,29201172,216164520,1484052570,
%T A382874 9607866268,59342703420,352648983960,2029131058500,11360419371000,
%U A382874 62125264788840,332868702695760,1751865025825530,9075126224864700,46353422502086700,233788539957892920
%N A382874 Expansion of g.f. 2-hypergeom([3/2,7/2],[-1/2],4*x).
%F A382874 a(0) = 1, a(n) = 8*4^n*(4*n^2 - 1)*Gamma(7/2 + n)/(15*sqrt(Pi)*n!), n>=1.
%F A382874 G.f.: 2 + (768*x^2 + 64*x - 1)/(1 - 4*x)^(11/2).
%F A382874 For n>=1, a(n) = (2*n-1) * (2*n+1)^2 * (2*n+3) * (2*n+5) * binomial(2*n,n)/15. - _Vaclav Kotesovec_, Apr 07 2025
%p A382874 seq(coeff(series(2-hypergeom([3/2, 7/2], [-1/2], 4*x), x, k+1), x, k), k=0..19);
%o A382874 (PARI) my(x='x+O('x^30)); Vec(2 - hypergeom([3/2,7/2],[-1/2],4*x)) \\ _Michel Marcus_, Apr 07 2025
%Y A382874 Cf. A002423, A001700, A002457, A002421.
%K A382874 nonn
%O A382874 0,2
%A A382874 _Karol A. Penson_, Apr 07 2025