OFFSET
0,2
COMMENTS
More generally, for integer m>=0 and real p and q,
exp( Sum_{n>=1} (p^n+q^n)^m*x^n/n ) = 1/Product_{k=0..m} (1 - p^k*q^(m-k)*x)^C(m,k).
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (25,-228,900,-1296).
FORMULA
O.g.f.: 1/((1-4*x)*(1-6*x)^2*(1-9*x)).
From Stefano Spezia, Jul 21 2022: (Start)
a(n) = 25*a(n-1) - 228*a(n-2) + 900*a(n-3) - 1296*a(n-4) for n > 3.
a(n) = (9^(2+n) - 4^(2+n) - 5*6^(1+n)*(2 + n))/5. (End)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, ((2^m+3^m)^2*x^m/m)+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul D. Hanna, Apr 22 2010
STATUS
approved