A325219 G.f. A(x) satisfies: Sum_{n>=0} x^n*A(x)^(n^2) = Sum_{n>=0} x^n/(1-n*x)^n.

1, 1, 1, 3, 14, 81, 554, 4175, 33894, 292482, 2658803, 25312031, 251337905, 2595476384, 27814372541, 308814996237, 3547597450937, 42121414823717, 516406224737906, 6531681539263289, 85162992707351910, 1143744473741844428, 15809784290241899546, 224756696173450416445, 3283701348287927969258, 49267186208121297961411, 758541179347396245098635, 11976195590135148979244826, 193765334786286246261399910

Offset: 0

Author

Paul D. Hanna, Apr 30 2019

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 14*x^4 + 81*x^5 + 554*x^6 + 4175*x^7 + 33894*x^8 + 292482*x^9 + 2658803*x^10 + 25312031*x^11 + 251337905*x^12 + ...
such that the following series are equal
B(x) = 1 + x*A(x) + x^2*A(x)^4 + x^3*A(x)^9 + x^4*A(x)^16 + x^5*A(x)^25 + x^6*A(x)^36 + x^7*A(x)^49 + x^8*A(x)^64 + ...
B(x) = 1 + x/(1-x) + x^2/(1-2*x)^2 + x^3/(1-3*x)^3 + x^4/(1-4*x)^4 + x^5/(1-5*x)^5 + x^6/(1-6*x)^6 + x^7/(1-7*x)^7 + x^8/(1-8*x)^8 + ...
where
B(x) = 1 + x + 2*x^2 + 6*x^3 + 23*x^4 + 104*x^5 + 537*x^6 + 3100*x^7 + 19693*x^8 + 136064*x^9 + 1013345*x^10 + 8076644*x^11 + ... + A080108(n)*x^n + ...
		

Crossrefs

Cf. A080108.

Programs

PARI

{a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0);
A[#A] = polcoeff( sum(m=0, #A, x^m*( 1/(1-m*x +x*O(x^#A))^m - Ser(A)^(m^2)) ), #A) ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))