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 A383948 #19 Aug 27 2025 09:14:39
%S A383948 1,8,51,308,1855,11340,70665,448320,2887155,18815240,123759097,
%T A383948 819969276,5464090177,36580917716,245837438055,1657396783440,
%U A383948 11204207037315,75918595916520,515462211835305,3506072423912940,23885410548196701,162951783575205108,1113110415733083531
%N A383948 Expansion of 1/sqrt((1-3*x)^3 * (1-7*x)).
%H A383948 Vincenzo Librandi, <a href="/A383948/b383948.txt">Table of n, a(n) for n = 0..500</a>
%F A383948 n*a(n) = (10*n-2)*a(n-1) - 21*n*a(n-2) for n > 1.
%F A383948 a(n) = (1/4)^n * Sum_{k=0..n} 3^k * 7^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k).
%F A383948 a(n) = Sum_{k=0..n} (-1)^k * 7^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(n+1,n-k).
%F A383948 a(n) = Sum_{k=0..n} 3^(n-k) * binomial(2*k,k) * binomial(n+1,n-k).
%t A383948 CoefficientList[Series[ 1/Sqrt[(1-3*x)^3*(1-7*x)],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 27 2025 *)
%o A383948 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-3*x)^3*(1-7*x)))
%o A383948 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/Sqrt((1- 3*x)^3 * (1-7*x)); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 27 2025
%Y A383948 Cf. A098409, A360318.
%Y A383948 Cf. A383949, A383950.
%Y A383948 Cf. A132894.
%K A383948 nonn,changed
%O A383948 0,2
%A A383948 _Seiichi Manyama_, Aug 19 2025