A136506 a(n) = binomial(2^n + 2, n).

1, 4, 15, 120, 3060, 278256, 90858768, 105637584000, 436355999662176, 6431591598617108352, 340881559632021623909760, 65533747894341651530074060800, 46081376018330435634530315478453248

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), A136505 (0,1), this sequence (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 +2, n): n in [0..20]]; // G. C. Greubel, Mar 14 2021

Maple

A136506:= n-> binomial(2^n+2,n); seq(A136506(n), n=0..20); # G. C. Greubel, Mar 14 2021

Mathematica

Table[Binomial[2^n+2,n],{n,0,20}] (* Harvey P. Dale, Jun 20 2011 *)

PARI

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

Sage

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

Formula

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

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