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

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

Offset

0,2

Links

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

Formula

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

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 *)

Prog

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

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.

Sequence in context: A339283 A095288 A155105 * A180966 A203032 A086812

Adjacent sequences: A132682 A132683 A132684 * A132686 A132687 A132688

Keyword

nonn

Author

Paul D. Hanna, Aug 26 2007

Status

approved