OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
FORMULA
a(n) = (2^n/n!) * Product_{k=0..n-1} (8*k + 1).
a(n) ~ 16^n/(GAMMA(1/8)*n^(7/8)). - Vaclav Kotesovec, Jul 24 2013
EXAMPLE
G.f.: A(x) = 1 + 2*x + 18*x^2 + 204*x^3 + 2550*x^4 + 33660*x^5 + ...
where
A(x)^8 = 1 + 16*x + 256*x^2 + 4096*x^3 + 65536*x^4 + ... + 16^n*x^n + ...
Also,
A(x)^4 = 1 + 8*x + 96*x^2 + 1280*x^3 + 17920*x^4 + 258048*x^5 + ... + 4^n*A000984(n)*x^n + ...
A(x)^2 = 1 + 4*x + 40*x^2 + 480*x^3 + 6240*x^4 + 84864*x^5 + ... + 2^n*A004981(n)*x^n + ...
MAPLE
seq(coeff(series(1/(1-16*x)^(1/8), x, 50), x, n+1), n=0..20); # Muniru A Asiru, Jun 23 2018
MATHEMATICA
CoefficientList[Series[1/(1-16*x)^(1/8), {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 24 2013 *)
PROG
(PARI) {a(n)=polcoeff(1/(1-16*x +x*O(x^n))^(1/8), n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=(2^n/n!)*prod(k=0, n-1, 8*k + 1)}
for(n=0, 30, print1(a(n), ", "))
(GAP) List([0..20], n->(2^n/Factorial(n))*Product([0..n-1], k->8*k+1)); # Muniru A Asiru, Jun 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 23 2013
STATUS
approved