A132687 a(n) = binomial(2^n + 3*n - 1, n).

1, 4, 36, 560, 17550, 1370754, 324540216, 267212177232, 822871715492970, 9728874233306696390, 442491588454024774291770, 76919746769405407508866898400, 50743487119356450255156023756871000

Offset: 0

Author

Paul D. Hanna, Aug 26 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..50

Crossrefs

Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), A014070 (0,0), A136505 (0,1), A136506 (0,2), A060690 (1,-1), A132683 (1,0), A132684 (1,1), A132685 (2,0), A132686 (2,1), this sequence (3,-1), A132688 (3,0), A132689 (3,1).

Cf. A136555.

Programs

Magma

[Binomial(2^n +3*n -1, n): n in [0..20]]; // G. C. Greubel, Mar 13 2021

Mathematica

Table[Binomial[2^n+3n-1,n],{n,0,20}] (* Harvey P. Dale, Sep 07 2017 *)

PARI

a(n)=binomial(2^n+3*n-1,n)

Sage

[binomial(2^n +3*n -1, n) for n in (0..20)] # G. C. Greubel, Mar 13 2021

Formula

a(n) = [x^n] 1/(1-x)^(2^n + 2*n).