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 A382274 #27 Apr 13 2025 03:10:22
%S A382274 1,10,90,730,5570,40762,289370,2007210,13671170,91750250,608294490,
%T A382274 3991833210,25968131010,167664187290,1075453670490,6858654320970,
%U A382274 43517809896450,274862176368330,1728960219827290,10835520927931930,67679638209628098,421442759107879930
%N A382274 Expansion of 1/(1 - 4*x/(1-x)^2)^(5/2).
%F A382274 a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (5-3*k/n) * (n-k) * a(k).
%F A382274 a(n) = ((7*n+3)*a(n-1) - (7*n-24)*a(n-2) + (n-3)*a(n-3))/n for n > 2.
%F A382274 a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(n+k-1,n-k).
%F A382274 a(n) = 10*n*hypergeom([7/2, 1-n, 1+n], [3/2, 2], -1) for n > 0. - _Stefano Spezia_, Mar 30 2025
%F A382274 a(n) ~ 2^(3/4) * n^(3/2) * (1 + sqrt(2))^(2*n) / (3*sqrt(Pi)). - _Vaclav Kotesovec_, Apr 13 2025
%o A382274 (PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-5/2, k)*binomial(n+k-1, n-k));
%Y A382274 Cf. A110170, A377198, A382332.
%Y A382274 Cf. A002802, A377199.
%K A382274 nonn
%O A382274 0,2
%A A382274 _Seiichi Manyama_, Mar 29 2025