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 A383946 #17 Aug 27 2025 18:21:45
%S A383946 1,14,159,1676,17005,168570,1645035,15873240,151863705,1443272870,
%T A383946 13643264503,128404376292,1204055841157,11255397745298,
%U A383946 104933302809795,976016662472880,9059771065058865,83945271527170110,776569280469986895,7173673630527966780,66182347507155379101,609866573826736447914
%N A383946 Expansion of 1/sqrt((1-9*x)^3 * (1-x)).
%H A383946 Vincenzo Librandi, <a href="/A383946/b383946.txt">Table of n, a(n) for n = 0..800</a>
%F A383946 a(n) = A331516(n) - A331516(n-1).
%F A383946 n*a(n) = (10*n+4)*a(n-1) - 9*n*a(n-2) for n > 1.
%F A383946 a(n) = (1/4)^n * Sum_{k=0..n} 9^k * (2*k+1) * binomial(2*k,k) * binomial(2*(n-k),n-k).
%F A383946 a(n) = Sum_{k=0..n} 2^k * (2*k+1) * binomial(2*k,k) * binomial(n+1,n-k).
%F A383946 a(n) = Sum_{k=0..n} (-2)^k * 9^(n-k) * binomial(2*k,k) * binomial(n+1,n-k).
%t A383946 CoefficientList[Series[1/Sqrt[(1-9*x)^3*(1-x)],{x,0,33}],x] (* _Vincenzo Librandi_, Aug 27 2025 *)
%o A383946 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-9*x)^3*(1-x)))
%o A383946 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/Sqrt((1- 9*x)^3 * (1-x)); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 27 2025
%Y A383946 Cf. A084771, A331516.
%K A383946 nonn,changed
%O A383946 0,2
%A A383946 _Seiichi Manyama_, Aug 19 2025