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 A002690 a(n) = (n+1) * (2*n)! / n!. (Formerly M3665 N1491) 4
 1, 4, 36, 480, 8400, 181440, 4656960, 138378240, 4670265600, 176432256000, 7374868300800, 337903056691200, 16838835658444800, 906706535454720000, 52459449551308800000, 3245491278907637760000, 213796737998040637440000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Coefficients of orthogonal polynomials. E.g.f. for series with alternating signs: x/(1+4*x)^(1/2). Central terms of triangle A245334. - Reinhard Zumkeller, Aug 30 2014 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177. H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177. [Annotated scanned copy] FORMULA E.g.f.: (1-2*x)/(1-4*x)^(3/2). MAPLE with(combstruct):bin := {B=Union(Z, Prod(B, B))}: seq (count([B, bin, labeled], size=n)*n, n=1..17); # Zerinvary Lajos, Dec 05 2007 MATHEMATICA Table[((n+1)(2n)!)/n!, {n, 0, 20}] (* Harvey P. Dale, Sep 04 2011 *) PROG (PARI) a(n)=(n+1)*(2*n)!/n! (Magma) [(n+1) * Factorial(2*n) /Factorial(n): n in [0..20]]; // Vincenzo Librandi, Sep 05 2011 (Haskell) a002690 n = a245334 (2 * n) n -- Reinhard Zumkeller, Aug 30 2014 CROSSREFS a(n) = (n+1) * A001813(n) = 2^n * A001193(n+1). Cf. A002691, A000407. Cf. A245334. Sequence in context: A135906 A197446 A291313 * A094417 A349504 A354264 Adjacent sequences: A002687 A002688 A002689 * A002691 A002692 A002693 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Edited by Ralf Stephan, Mar 21 2004 STATUS approved

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Last modified March 30 00:49 EDT 2023. Contains 361599 sequences. (Running on oeis4.)