OFFSET
0,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
a(n) = (1/n)*Sum_{k=1..n} 2^(k^2-k+1) * a(n-k) for n>0, with a(0)=1.
a(n) ~ 2^(n^2 - n + 1) / n. - Vaclav Kotesovec, Oct 07 2020
EXAMPLE
G.f.: A(x) = 1 + 2*x + 6*x^2 + 52*x^3 + 2150*x^4 + 423804*x^5 + ...
log(A(x)) = 2*x + 2^3*x^2/2 + 2^7*x^3/3 + 2^13*x^4/4 + 2^21*x^5/5 + 2^31*x^6/6 + ...
PROG
(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 2^(k^2-k+1)*x^k/k)+x*O(x^n)), n)}
for(n=0, 15, print1(a(n), ", "))
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, 2^(k^2-k+1)*a(n-k)))}
for(n=0, 15, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 08 2009
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, Jan 05 2020
STATUS
approved