OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..80
FORMULA
a(n) = Sum_{k=0..n} C(n,k)*[(4^k-1)/3]^(n-k).
a(n) ~ c * 2^(n^2/2+n+1/2)/(3^(n/2)*sqrt(Pi*n)), where c = Sum_{k = -infinity..infinity} 3^k*4^(-k^2) = 1.86902676808473931... if n is even and c = Sum_{k = -infinity..infinity} 3^(k+1/2)*4^(-(k+1/2)^2) = 1.87384213421283135... if n is odd. - Vaclav Kotesovec, Jun 25 2013
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*((4^k-1)/3)^(n-k), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jun 25 2013 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(n, k)*((4^k-1)/3)^(n-k))
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp((4^k-1)/3*x)*x^k/k!), n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 27 2007
STATUS
approved