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 A382537 #17 Apr 02 2025 04:16:48
%S A382537 1,1,11,51,211,1061,4923,22765,107687,502479,2352231,11022911,
%T A382537 51590795,241559783,1131156175,5295875131,24797055115,116104311885,
%U A382537 543622665219,2545347081565,11917847333151,55801588711565,261274518155435,1223337818786305,5727913381451455
%N A382537 Expansion of 1/(1 - x*(1 + 4*x)^(5/2)).
%H A382537 Vincenzo Librandi, <a href="/A382537/b382537.txt">Table of n, a(n) for n = 0..300</a>
%F A382537 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(5*k/2,n-k).
%t A382537 Table[Sum[4^(n-k)*Binomial[5*k/2,n-k],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Apr 02 2025 *)
%o A382537 (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(5*k/2, n-k));
%o A382537 (Magma) R<x> := PowerSeriesRing(Rationals(), 40); f := 1/(1 - x*(1 + 4*x)^(5/2)); seq := [ Coefficient(f, n) : n in [0..30] ];seq; // _Vincenzo Librandi_, Apr 02 2025
%Y A382537 Cf. A362154, A382536, A382538.
%Y A382537 Cf. A002422, A382515.
%K A382537 nonn,easy
%O A382537 0,3
%A A382537 _Seiichi Manyama_, Mar 31 2025