A002803 a(n) = (2n+4)!/(4!*n!*(n+1)!). (Formerly M4980 N2140)

1, 15, 140, 1050, 6930, 42042, 240240, 1312740, 6928350, 35565530, 178474296, 878850700, 4259045700, 20359174500, 96172862400, 449608131720, 2082743551350, 9569730173850, 43651400793000, 197809768856700, 891085911135420, 3992527783658700, 17800677233071200

Offset

0,2

References

Charles Jordan, Calculus of Finite Differences, Budapest, 1939, p. 449.

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

T. D. Noe, Table of n, a(n) for n = 0..200

T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

Formula

From R. J. Mathar, Aug 09 2015: (Start)

G.f.: 2F1(5/2,3;2;4x) = (1+x)/(1-4x)^(7/2).

a(n) = A020918(n) + A020918(n-1). (End).

D-finite with recurrence n*(n+1)*a(n) - 2*(n+2)*(2*n+3)*a(n-1) = 0. - R. J. Mathar, Feb 08 2021

a(n) ~ 2^(2*n+1) * n^(5/2) / (3 * exp(5/n) * sqrt(Pi)). - Amiram Eldar, Sep 22 2025

Mathematica

Table[(2*n+4)!/(4!*n!*(n+1)!), {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Dec 13 2008 *)

Crossrefs

Cf. A020918.

Sequence in context: A302855 A133716 A035330 * A354394 A346977 A354398

Adjacent sequences: A002800 A002801 A002802 * A002804 A002805 A002806

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved