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A085374
a(n) = binomial(2n+1, n+1)*binomial(n+3, 3).
2
1, 12, 100, 700, 4410, 25872, 144144, 772200, 4011150, 20323160, 100876776, 492156392, 2366136500, 11232648000, 52739956800, 245240799120, 1130632213590, 5172827121000, 23504600427000, 106141827191400
OFFSET
0,2
FORMULA
a(n) = A000292(n+1)*A000984(n+1)/2. - Zerinvary Lajos, Jan 18 2007, corrected Aug 09 2015
D-finite with recurrence n*(n+1)*a(n) - 2*(n+3)*(2*n+1)*a(n-1) = 0. - R. J. Mathar, Aug 09 2015
G.f.: 2F1(3/2,4;2;4x). - R. J. Mathar, Aug 09 2015
MAPLE
seq(binomial(n+2, 3)/2*binomial(2*n, n), n=1..20); # Zerinvary Lajos, Jan 18 2007
MATHEMATICA
Table[Binomial[2 n + 1, n + 1]Binomial[n + 3, 3], {n, 0, 30}]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Jun 26 2003
STATUS
approved