OFFSET
0,5
COMMENTS
FORMULA
a(n) = Sum_{k=0..[n/4]} n!/[k!*(n-4*k)!*4^k] * a(k), with a(0)=1.
EXAMPLE
E.g.f. A(x) = exp( x + x^4/4 + x^16/4^5 + x^64/3^21 + x^256/3^85 +..)
= 1 + 1*x + 1*x^2/2! + 1*x^3/3! + 7*x^4/4! + 31*x^5/5!+ 91*x^6/6!+...
PROG
(PARI) a(n)=if(n==0, 1, sum(k=0, n\4, n!/(k!*(n-4*k)!*4^k)*a(k)))
(PARI) /* Defined by E.G.F.: */ a(n)=n!*polcoeff( exp(sum(k=0, ceil(log(n+1)/log(4)), x^(4^k)/4^((4^k-1)/3))+x*O(x^n)), n, x)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 06 2006
STATUS
approved