OFFSET
0,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..500
FORMULA
G.f.: Sum_{n>=0} x^n * (1+x)^(n^2) / (1 - x*(1+x)^n)^(n+1).
G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k) * (1+x)^(n*k).
a(n) = Sum_{j=0..n} Sum_{k=0..n-j} binomial(n-j, k) * binomial((n-j)*k, j).
EXAMPLE
G.f.: A(x) = 1 + 2*x + 5*x^2 + 16*x^3 + 60*x^4 + 254*x^5 + 1188*x^6 + 6043*x^7 + 33080*x^8 + 193249*x^9 + 1197001*x^10 + ...
such that
A(x) = 1 + (1 + (1+x))*x + (1 + (1+x)^2)^2*x^2 + (1 + (1+x)^3)^3*x^3 + (1 + (1+x)^4)^4*x^4 + (1 + (1+x)^5)^5*x^5 + (1 + (1+x)^6)^6*x^6 + ...
PROG
(PARI) {a(n) = my(A=1); A = sum(k=0, n, (1 + (1+x)^k +x*O(x^n))^k * x^k ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n) = sum(j=0, n, sum(k=0, n-j, binomial(n-j, k) * binomial((n-j)*k, j) ))}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 21 2018
STATUS
approved