A199747 a(n) = binomial(n*(3*n+1)/2, n).

1, 2, 21, 455, 14950, 658008, 36288252, 2404808340, 186087894300, 16466440817750, 1639875152957965, 181513211783531667, 22105238818111121361, 2937279723907795168000, 422879027090638497044400, 65572027180886570401929144, 10894880155433107077641916792

Offset

0,2

Comments

a(5*n+3) is divisible by 5; a(5*n+4) is divisible by 5.

Links

G. C. Greubel, Table of n, a(n) for n = 0..300

Formula

a(n) = C(n*(3*n+1)/2, n*(3*n-1)/2) = C(A005449(n), A000326(n)), where A000326 and A005449 are pentagonal numbers.

a(n) ~ n^(n-1/2) * exp(n) * 3^n / (sqrt(Pi) * 2^(n+1/2)). - Vaclav Kotesovec, Apr 23 2015

Mathematica

Table[Binomial[(n(3n+1))/2, n], {n, 0, 20}] (* Harvey P. Dale, Apr 14 2015 *)

Prog

(PARI) a(n)=binomial(n*(3*n+1)/2, n)

Crossrefs

Cf. A199748, A000326, A005449, A001318.

Sequence in context: A024232 A192666 A090451 * A303867 A238696 A226057

Adjacent sequences: A199744 A199745 A199746 * A199748 A199749 A199750

Keyword

nonn,easy

Author

Paul D. Hanna, Nov 09 2011

Status

approved