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 A002690 M3665 N1491 #43 Jan 22 2025 11:31:50
%S A002690 1,4,36,480,8400,181440,4656960,138378240,4670265600,176432256000,
%T A002690 7374868300800,337903056691200,16838835658444800,906706535454720000,
%U A002690 52459449551308800000,3245491278907637760000,213796737998040637440000,14940619102451310428160000,1103945744792235714969600000
%N A002690 a(n) = (n+1) * (2*n)! / n!.
%C A002690 Coefficients of orthogonal polynomials.
%C A002690 E.g.f. for series with alternating signs: x/(1+4*x)^(1/2).
%C A002690 Central terms of triangle A245334. - _Reinhard Zumkeller_, Aug 30 2014
%D A002690 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002690 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002690 Vincenzo Librandi, <a href="/A002690/b002690.txt">Table of n, a(n) for n = 0..200</a>
%H A002690 H. E. Salzer, <a href="http://dx.doi.org/10.1090/S0025-5718-1955-0078498-1">Orthogonal polynomials arising in the evaluation of inverse Laplace transforms</a>, Math. Comp. 9 (1955), 164-177.
%H A002690 H. E. Salzer, <a href="/A000407/a000407.pdf">Orthogonal polynomials arising in the evaluation of inverse Laplace transforms</a>, Math. Comp. 9 (1955), 164-177. [Annotated scanned copy]
%F A002690 E.g.f.: (1-2*x)/(1-4*x)^(3/2).
%F A002690 a(n) = 2^n*n!*JacobiP(n, -1/2, -n+1, 3). - _Peter Luschny_, Jan 22 2025
%p A002690 with(combstruct):bin := {B=Union(Z,Prod(B,B))}:
%p A002690 seq (count([B,bin,labeled],size=n+1)*(n+1), n=0..17); # _Zerinvary Lajos_, Dec 05 2007
%p A002690 A002690 := n -> 2^n*n!*JacobiP(n, -1/2, -n+1, 3):
%p A002690 seq(simplify(A002690(n)), n = 0..18); # _Peter Luschny_, Jan 22 2025
%t A002690 Table[((n+1)(2n)!)/n!,{n,0,20}] (* _Harvey P. Dale_, Sep 04 2011 *)
%o A002690 (PARI) a(n)=(n+1)*(2*n)!/n!
%o A002690 (Magma) [(n+1) * Factorial(2*n) /Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Sep 05 2011
%o A002690 (Haskell)
%o A002690 a002690 n = a245334 (2 * n) n -- _Reinhard Zumkeller_, Aug 30 2014
%Y A002690 a(n) = (n+1) * A001813(n) = 2^n * A001193(n+1).
%Y A002690 Cf. A002691, A000407.
%Y A002690 Cf. A245334.
%K A002690 nonn,easy,nice
%O A002690 0,2
%A A002690 _N. J. A. Sloane_
%E A002690 Edited by _Ralf Stephan_, Mar 21 2004