OFFSET
0,2
FORMULA
G.f.: (1-x)^2 * Sum_{n>=0} (2*n+1) * x^n * (1 + (1-x)^2)^(n*(n+1)/2).
EXAMPLE
G.f.: A(x) = 1 + 4*x + 23*x^2 + 269*x^3 + 6080*x^4 + 263107*x^5 + 21755790*x^6 + 3448734174*x^7 + 1054337703035*x^8 + ...
such that
A(x)/(1-x)^2 = 1 + 3*x*(2-2*x+x^2) + 5*x^2*(2-2*x+x^2)^3 + 7*x^3*(2-2*x+x^2)^6 + 9*x^4*(2-2*x+x^2)^10 + 11*x^5*(2-2*x+x^2)^15 + 13*x^6*(2-2*x+x^2)^21 +...
PROG
(PARI) {a(n) = my(A = (1-x)^2 * sum(m=0, n, (2*m+1) * x^m * (1 + (1-x)^2 +x*O(x^n) )^(m*(m+1)/2) ) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 30 2018
STATUS
approved