A132685 -id:A132685 - cp's OEIS frontend

A132688 a(n) = binomial(2^n + 3*n, n).

1, 5, 45, 680, 20475, 1533939, 350161812, 280384608504, 847073824772175, 9894081531608130857, 446730013630787463700695, 77328499046923986969058944720, 50891283683781760304442885961988100

Offset: 0

Paul D. Hanna, Aug 26 2007

nonn

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

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), this sequence (3,0), A132689 (3,1).

Cf. A136555.

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

Table[Binomial[2^n+3n,n],{n,0,20}] (* Harvey P. Dale, Oct 30 2018 *)

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

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

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

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

Original entry on oeis.org

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

Offset: 0

Paul D. Hanna, Aug 26 2007

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

Cf. A136555.

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

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

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)
```

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

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

cp's OEIS Frontend

A132688 a(n) = binomial(2^n + 3*n, n).

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