A132689 a(n) = binomial(2^n + 3*n + 1, n).

1, 6, 55, 816, 23751, 1712304, 377447148, 294109729200, 871896500955975, 10061777828754031380, 451004941990890693018405, 77739225019650285306412710240, 51039474754930845750609669420261300

Offset: 0

Author

Paul D. Hanna, Aug 26 2007

Keywords

• nonn
• easy

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

Cf. A136555.

Programs

Magma

[Binomial(2^n+3*n+1, n) : n in [0..15]]; // Wesley Ivan Hurt, Nov 20 2014

Maple

A132689:=n->binomial(2^n+3*n+1, n): seq(A132689(n), n=0..15); # Wesley Ivan Hurt, Nov 20 2014

Mathematica

Table[Binomial[2^n +3n +1, n], {n, 0, 15}] (* Wesley Ivan Hurt, Nov 20 2014 *)

PARI

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

Sage

[binomial(2^n +3*n+1, n) for n in (0..15)] # G. C. Greubel, Feb 15 2021

Formula

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