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A000911
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a(n) = (2n+3)! /( n! * (n+1)! ).
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5
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6, 60, 420, 2520, 13860, 72072, 360360, 1750320, 8314020, 38798760, 178474296, 811246800, 3650610600, 16287339600, 72129646800, 317370445920, 1388495700900, 6044040109800, 26190840475800, 113034153632400, 486046860619320, 2083057974082800, 8900338616535600
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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REFERENCES
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E. R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, 1975, p. 99.
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LINKS
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FORMULA
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G.f.: 6*(1+10*x/( G(0)- 10*x)), where G(k)= 2*x*(2*k+5) + k + 1 - 2*x*(k+1)*(2*k+7)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jul 14 2013
G.f.: 6/(1 - 4*x)^(5/2).
a(n) ~ 2^(2*n+3)*n^(3/2)/sqrt(Pi). (End)
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EXAMPLE
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6 + 60*x + 420*x^2 + 2520*x^3 + 13860*x^4 + 72072*x^5 + 360360*x^6 + ...
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MAPLE
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seq(binomial(2*n, n)*binomial(n, (n-2)), n=2..21); # Zerinvary Lajos, May 10 2007
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MATHEMATICA
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Table[(2 n + 3)!/(n!*(n + 1)!), {n, 0, 20}] (* T. D. Noe, Jun 20 2012 *)
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PROG
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(PARI) a(n) = 2^(n+4)*polcoeff(pollegendre(n+4), n) /* Ralf Stephan */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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