OFFSET
0,2
EXAMPLE
E.g.f.: A(x) = 1 + 6*x + 88*x^2/2! + 2160*x^3/3! + 76336*x^4/4! + 3594112*x^5/5! + 214575872*x^6/6! + 15695861760*x^7/7! + 1371486918144*x^8/8! +...
where
A(x)*exp(2) = 1 + 2*(1+x) + 2^2*(1+x)^4/2! + 2^3*(1+x)^9/3! + 2^4*(1+x)^16/4! + 2^5*(1+x)^25/5! + 2^6*(1+x)^36/6! + 2^7*(1+x)^49/7! + 2^8*(1+x)^64/8! +...
PROG
(PARI) /* Quick print of terms 0..30: */
\p80
Vec(round( serlaplace( sum(n=0, 400, 2^n * (1+x +O(x^31))^(n^2) /n! *1.)/exp(2) ) ))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 04 2016
STATUS
approved