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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• C. 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.

Crossrefs

Cf. A020918.

Programs

Mathematica

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

Formula

G.f.: 2F1(5/2,3;2;4x) =(1+x)/(1-4x)^(7/2). - R. J. Mathar, Aug 09 2015

a(n) = A020918(n)+A020918(n-1). - R. J. Mathar, Aug 09 2015

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