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 A050476 #36 Aug 23 2025 09:19:34
%S A050476 1,7,26,95,350,1302,4884,18447,70070,267410,1024556,3938662,15184876,
%T A050476 58689100,227327400,882230895,3429693990,13353413370,52062618300,
%U A050476 203235266850,794258570820,3107215911540,12167180964120,47685286297350,187036101361980,734153906619252,2883674432327864,11333968799308652
%N A050476 a(n) = C(n)*(6*n + 1) where C(n) = Catalan numbers (A000108).
%D A050476 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A050476 Andrew Howroyd, <a href="/A050476/b050476.txt">Table of n, a(n) for n = 0..200</a>
%F A050476 5*(n+1)*a(n) + 2*(-14*n-1)*a(n-1) + 16*(2*n-3)*a(n-2) = 0. - _R. J. Mathar_, Feb 04 2015
%F A050476 G.f.: (5 - 8*x - 5*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - _Ilya Gutkovskiy_, Jun 13 2017
%F A050476 From _Peter Bala_, Aug 23 2025: (Start)
%F A050476 a(n) = binomial(2*n, n) + 5*binomial(2*n, n-1) = A000984(n) + 5*A001791(n).
%F A050476 a(n) ~ 4^n * 6/sqrt(Pi*n). (End)
%t A050476 Table[CatalanNumber[n](6n+1),{n,0,20}] (* _Harvey P. Dale_, Nov 05 2011 *)
%o A050476 (Magma) [Catalan(n)*(6*n+1):n in [0..27] ]; // _Marius A. Burtea_, Jan 05 2020
%o A050476 (Magma) R<x>:=PowerSeriesRing(Rationals(),30); (Coefficients(R!( (5-8*x-5*Sqrt(1-4*x))/(2*x*Sqrt(1-4*x))))); // _Marius A. Burtea_, Jan 05 2020
%Y A050476 Column k=6 of A330965.
%Y A050476 Cf. A016861, A000108, A051945.
%K A050476 easy,nonn,changed
%O A050476 0,2
%A A050476 _Barry E. Williams_, Dec 24 1999