OFFSET
0,2
FORMULA
a(n) = (2^n/n!) * Product_{k=0..n-1} (16*k + 1).
a(n) ~ 32^n/(GAMMA(1/16)*n^(15/16)). - Vaclav Kotesovec, Jul 24 2013
EXAMPLE
G.f.: A(x) = 1 + 2*x + 34*x^2 + 748*x^3 + 18326*x^4 + 476476*x^5 +...
where
A(x)^16 = 1 + 32*x + 1024*x^2 + 32768*x^3 + 1048576*x^4 +...+ 32^n*x^n +...
Also,
A(x)^8 = 1 + 16*x + 384*x^2 + 10240*x^3 + 286720*x^4 +...+ 8^n*A000984(n)*x^n +...
A(x)^4 = 1 + 8*x + 160*x^2 + 3840*x^3 + 99840*x^4 +...+ 4^n*A004981(n)*x^n +...
A(x)^2 = 1 + 4*x + 72*x^2 + 1632*x^3 + 40800*x^4 +...+ 2^n*A224881(n)*x^n +...
MATHEMATICA
CoefficientList[Series[1/(1-32*x)^(1/16), {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 24 2013 *)
PROG
(PARI) {a(n)=polcoeff(1/(1-32*x +x*O(x^n))^(1/16), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=(2^n/n!)*prod(k=0, n-1, 16*k + 1)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 23 2013
STATUS
approved