OFFSET
0,3
COMMENTS
Conjecture: For all integers m > 0, Sum_{n>=0} L(n)^m * log(1+x)^n/n! is an integer series whenever Sum_{n>=0} L(n)*log(1+x)^n/n! is an integer series.
FORMULA
a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*A167137(k)^2. - Vladeta Jovovic, Nov 08 2009
EXAMPLE
G.f.: A(x) = 1 + x + 12*x^2 + 148*x^3 + 2523*x^4 + ...
Illustrate A(x) = Sum_{n>=0} A167137(n)^2*log(1+x)^n/n!:
A(x) = 1 + log(1+x) + 5^2*log(1+x)^2/2! + 31^2*log(1+x)^3/3! + 257^2*log(1+x)^4/4! + ...
where P(x), the partition function of A000041, is generated by:
P(x) = 1 + log(1+x) + 5*log(1+x)^2/2! + 31*log(1+x)^3/3! + 257*log(1+x)^4/4! + ...
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 03 2009
STATUS
approved