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 + 1).
G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)*n!). - Paul D. Hanna, Feb 25 2009
a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016
EXAMPLE
From Paul D. Hanna, Feb 25 2009: (Start)
G.f.: A(x) = 1 + 3*x + 15*x^2 + 165*x^3 + 4845*x^4 + 435897*x^5 + ...
A(x) = 1/(1-x) - log(1-2x)/(1-2x) + log(1-4x)^2/((1-4x)*2!) - log(1-8x)^3/((1-8x)*3!) +- ... (End)
MAPLE
MATHEMATICA
Table[Binomial[2^n+n, n], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(PARI) a(n)=binomial(2^n+n, n)
(PARI) {a(n)=polcoeff(sum(m=0, n, (-log(1-2^m*x))^m/((1-2^m*x +x*O(x^n))*m!)), n)} \\ Paul D. Hanna, Feb 25 2009
(Sage) [binomial(2^n +n, n) for n in (0..20)] # G. C. Greubel, Mar 14 2021
(Magma) [Binomial(2^n +n, n): n in [0..20]]; // G. C. Greubel, Mar 14 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 26 2007
STATUS
approved