A113857 a(n) = binomial(4+2*n, n) * binomial(9+2*n, 4+n).

126, 2772, 48048, 772200, 12033450, 184940756, 2824549728, 43028530272, 655081791000, 9977399586000, 152112583402560, 2322021633001200, 35496198345658050, 543418421128852500, 8331507823355640000, 127919340117331963200, 1966759854303978934200, 30279186980267369086800

Offset

0,1

Comments

If one uses the "table" view of array A062190, the sequence appears as the fourth column right from the middle in the "formatted as a triangular array" subpanel.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Formula

a(n) = A062190(4+2*n, 4+n).

a(n) = A002694(n+2)*A001700(n+4). - R. J. Mathar, Nov 28 2008

a(n) ~ 2^(4*n+13) / (Pi*n). - Amiram Eldar, Sep 05 2025

Example

a(0) = C(4+2*n,n)*C(9+2*n,4+n) = C(4,0)*C(9,4) = 1*126 = 126.
a(7) = C(4+2*7,7)*C(9+2*7,4+7) = C(18,7)*C(23,11) = 31824*1352078 = 43028530272.

Mathematica

a[n_] := Binomial[4+2*n, n] * Binomial[9+2*n, 4+n]; Array[a, 20, 0] (* Amiram Eldar, Sep 05 2025 *)

Prog

(PARI) a(n)={binomial(4+2*n, n) * binomial(9+2*n, 4+n)} \\ Andrew Howroyd, Jan 07 2020

Crossrefs

Cf. A001700, A002694, A062190.

Sequence in context: A133499 A219005 A202398 * A267282 A008397 A329754

Adjacent sequences: A113854 A113855 A113856 * A113858 A113859 A113860

Keyword

easy,nonn

Author

Zerinvary Lajos, Feb 02 2006

Extensions

Definition rephrased by R. J. Mathar, Nov 28 2008

Edited and more terms added by Andrew Howroyd, Jan 07 2020

Status

approved