A136505 a(n) = binomial(2^n + 1, n).

1, 3, 10, 84, 2380, 237336, 82598880, 99949406400, 422825581068000, 6318976181520699840, 337559127276933693852160, 65182103393445184131620004864, 45946437874792132748338425828443136

Offset: 0

Author

Paul D. Hanna, Jan 01 2008

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

Cf. A136507, A136555.

Programs

Magma

[Binomial(2^n +1, n): n in [0..20]]; // G. C. Greubel, Mar 14 2021

Maple

A136505:= n-> binomial(2^n+1,n); seq(A136505(n), n=0..20); # G. C. Greubel, Mar 14 2021

Mathematica

Table[Binomial[2^n+1,n], {n,0,15}] (* Vaclav Kotesovec, Jul 02 2016 *)

PARI

{a(n)=polcoeff(sum(i=0,n,(1+2^i*x +x*O(x^n))*log(1+2^i*x +x*O(x^n))^i/i!),n)}

Sage

[binomial(2^n +1, n) for n in (0..20)] # G. C. Greubel, Mar 14 2021

Formula

G.f.: A(x) = Sum_{n>=0} (1 + 2^n*x) * log(1 + 2^n*x)^n/n!.

a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016