OFFSET
0,2
FORMULA
G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k) * (1+x)^(n*(n-k)) * (1+2*x)^(n*k).
EXAMPLE
G.f.: A(x) = 1 + 2*x + 7*x^2 + 32*x^3 + 180*x^4 + 1142*x^5 + 8162*x^6 + 63807*x^7 + 541202*x^8 + 4926969*x^9 + 47799429*x^10 + ...
such that
A(x) = 1 + ((1+x) + (1+2*x))*x + ((1+x)^2 + (1+2*x)^2)^2*x^2 + ((1+x)^3 + (1+2*x)^3)^3*x^3 + ((1+x)^4 + (1+2*x)^4)^4*x^4 + ((1+x)^5 + (1+2*x)^5)^5*x^5 + ...
PROG
(PARI) {a(n) = my(A=1); A = sum(k=0, n, ((1+x)^k + (1+2*x)^k +x*O(x^n))^k * x^k ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 24 2018
STATUS
approved