A132685 a(n) = binomial(2^n + 2*n, n).

1, 4, 28, 364, 10626, 850668, 218618940, 198773423848, 669741609663270, 8493008777332033900, 405943250253048290447028, 72938914603968404495709630360, 49143490709866058459392200362497820

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), this sequence (2,0), A132686 (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).

Cf. A136555.

Programs

Magma

[Binomial(2^n+2*n,n): n in [0..20]]; // G. C. Greubel, Mar 14 2021

Maple

A132695:= n-> binomial(2^n +2*n,n); seq(A132685(n), n=0..20); # G. C. Greubel, Mar 14 2021

Mathematica

Table[Binomial[2^n+2n,n],{n,0,20}] (* Harvey P. Dale, Jun 01 2016 *)

PARI

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

Sage

[binomial(2^n+2*n,n) for n in (0..20)] # G. C. Greubel, Mar 14 2021

Formula

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