OFFSET
0,3
COMMENTS
Trinomial coefficients satisfy: Sum_{k=0..2*n} A027907(n,k)*x^k = (1+x+x^2)^n.
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 13*x^4 + 34*x^5 + 93*x^6 +...
The logarithm begins:
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 31*x^4/4 + 91*x^5/5 + 282*x^6/6 + 890*x^7/7 + 2831*x^8/8 + 9055*x^9/9 + 29133*x^10/10 +...
which equals the sum of the series:
log(A(x)) = (1 + x + x^2)*x
+ (1 + 2^2*x + 3^2*x^2 + 2^2*x^3 + x^4)*x^2/2
+ (1 + 3^2*x + 6^2*x^2 + 7^2*x^3 + 6^2*x^4 + 3*x^5 + x^6)*x^3/3
+ (1 + 4^2*x + 10^2*x^2 + 16^2*x^3 + 19^2*x^4 + 16^2*x^5 + 10^2*x^6 + 4^2*x^7 + x^8)*x^4/4
+ (1 + 5^2*x + 15^2*x^2 + 30^2*x^3 + 45^2*x^4 + 51^2*x^5 + 45^2*x^6 + 30^2*x^7 + 15^2*x^8 + 5^2*x^9 + x^10)*x^5/5 +...
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 19 2011
STATUS
approved