A157135 G.f. satisfies: A(x) = Sum_{n>=0} x^(n^2) * A(x)^(n^2+n).

1, 1, 2, 5, 15, 50, 177, 649, 2437, 9322, 36214, 142546, 567409, 2280246, 9238883, 37699021, 154783906, 638983998, 2650697658, 11043733080, 46192300706, 193892210528, 816486626337, 3448376227978, 14603301098654, 61996178908151

Offset: 0

Author

Paul D. Hanna, Feb 24 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 50*x^5 + 177*x^6 +...
A(x)^2 = 1 + 2*x + 5*x^2 + 14*x^3 + 44*x^4 + 150*x^5 + 539*x^6 +...
A(x)^6 = 1 + 6*x + 27*x^2 + 110*x^3 + 435*x^4 + 1716*x^5 +...
A(x)^12 = 1 + 12*x + 90*x^2 + 544*x^3 + 2919*x^4 + 14592*x^5 +...
where
A(x) = 1 + x*A(x)^2 + x^4*A(x)^6 + x^9*A(x)^12 + x^16*A(x)^20 +...
		

Crossrefs

Cf. A157134, A157133, A157136.

Programs

PARI

{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,(A=sum(m=0,sqrtint(n),x^(m^2)*A^(m*(m+1)))));polcoeff(A,n)}

Formula

G.f. satisfies: A(x) = B(x*A(x)) where B(x) = A(x/B(x)) = g.f. of A157134,

where A157134(n) = [x^n] -1/A(x)^(n-1)/(n-1) for n>1,

and a(n) = [x^n] B(x)^(n+1)/(n+1) for n>=0.