A132686 a(n) = binomial(2^n + 2*n + 1, n).

1, 5, 36, 455, 12650, 962598, 237093780, 209004408899, 689960224294614, 8639439963148103450, 409865407260324119340236, 73328394245057556170201283726, 49287010273876375495535472789937580

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), this sequence (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).

Cf. A136555.

Programs

Magma

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

Mathematica

Table[Binomial[2^n +2*n +1, n], {n,0,20}] (* G. C. Greubel, Mar 13 2021 *)

PARI

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

Sage

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

Formula

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