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 A387367 #16 Aug 29 2025 10:15:33
%S A387367 1,25,435,6475,88270,1137150,14081970,169370850,1991916135,
%T A387367 23013193775,262062237437,2948690451525,32845189782860,
%U A387367 362721036253100,3975956599494420,43300257350934900,468875116313950845,5051523021827188725,54177811767428268535,578700942412768257775
%N A387367 Expansion of 1/(1 - 10*x + x^2)^(5/2).
%H A387367 Vincenzo Librandi, <a href="/A387367/b387367.txt">Table of n, a(n) for n = 0..1000</a>
%F A387367 n*a(n) = 5*(2*n+3)*a(n-1) - (n+3)*a(n-2) for n > 1.
%F A387367 a(n) = (binomial(n+4,2)/6) * A387369(n).
%F A387367 a(n) = (-1)^n * Sum_{k=0..n} (1/10)^(n-2*k) * binomial(-5/2,k) * binomial(k,n-k).
%t A387367 CoefficientList[Series[1/(1-10*x+x^2)^(5/2),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 29 2025 *)
%o A387367 (PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-10*x+x^2)^(5/2))
%o A387367 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/(1 - 10*x + x^2)^(5/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 29 2025
%Y A387367 Cf. A000332, A387341.
%Y A387367 Cf. A387369.
%K A387367 nonn,new
%O A387367 0,2
%A A387367 _Seiichi Manyama_, Aug 27 2025