OFFSET
0,3
COMMENTS
It appears that this sequence is integer valued.
The o.g.f. A(x) = 1 + x + 4*x^2 + 44*x^3 + ... for this sequence is such that 1 + x*d/dx( log(A(x) ) is the o.g.f. for A094088.
This sequence is the particular case m = 1 of the following general conjecture.
Let m be an integer and consider the sequence u(n) defined by the recurrence u(n) = m*Sum_{k = 0..n-1} binomial(2*n,2*k) *u(k) with the initial condition u(0) = 1. Then the expansion of exp( Sum_{n >= 1} u(n)*x^n/n ) ) has integer coefficients.
Note that u(n), as a polynomial in the variable m, is the n-th row generating polynomial of A241171.
FORMULA
O.g.f.: exp(x + 7*x^2/2 + 121*x^3/3 + 3907*x^4/4 + ...) = 1 + x + 4*x^2 + 44*x^3 + 1025*x^4 + ....
a(0) = 1 and a(n) = 1/n*Sum_{k = 0..n-1} A094088(n-k)*a(k) for n >= 1.
MAPLE
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Mar 11 2015
STATUS
approved