A114251 a(n) = C(3+2*n,3+n)*C(8+2*n,0+n).

1, 50, 1386, 30576, 600600, 11027016, 193993800, 3316739712, 55588369122, 918398981500, 15013703965260, 243495727020000, 3925151119562400, 62976611010020400, 1006711677146430000, 16046173576808179200, 255175067057177767500, 4050491847815341688760

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

From Amiram Eldar, Sep 06 2025: (Start)

a(n) = A002054(n+1) * A004310(n+4).

a(n) ~ 2^(4*n+11) / (Pi*n). (End)

Example

If n=0 then C(3+2*0,3+0)*C(8+2*0,0+0) = C(3,3)*C(8,0) = 1*1 = 1.
If n=7 then C(3+2*7,3+7)*C(8+2*7,0+7) = C(17,10)*C(22,7) = 19448*170544 = 3316739712.

Mathematica

Table[Binomial[3+2n, 3+n]Binomial[8+2n, n], {n, 0, 20}] (* Harvey P. Dale, Jul 26 2019 *)

Crossrefs

Cf. A002054, A004310, A062190.

Sequence in context: A031602 A231743 A140520 * A004351 A229316 A159177

Adjacent sequences: A114248 A114249 A114250 * A114252 A114253 A114254

Keyword

easy,nonn

Author

Zerinvary Lajos, Feb 04 2006

Extensions

More terms from Harvey P. Dale, Jul 26 2019

Status

approved