A337850 G.f. A(x) satisfies: Sum_{n>=0} x^(n^2) * A(x)^n = Sum_{n>=0} x^n * (1+x)^(n^2).

1, 2, 5, 15, 53, 217, 973, 4735, 24686, 137026, 805273, 4986541, 32409056, 220327688, 1562196894, 11522725486, 88215618320, 699573288808, 5736354452771, 48556636776122, 423674461139747, 3805446588538974, 35142868684678717, 333303148345306269, 3243121812554272131

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 15*x^3 + 53*x^4 + 217*x^5 + 973*x^6 + 4735*x^7 + 24686*x^8 + 137026*x^9 + 805273*x^10 + ...
such that the following series are equal
B(x) = 1 + x*A(x) + x^4*A(x)^2 + x^9*A(x)^3 + x^16*A(x)^4 + x^25*A(x)^5 + x^36*A(x)^6 + x^49*A(x)^7 + ... + x^(n^2)*A(x)^n + ...
B(x) = 1 + x*(1+x) + x^2*(1+x)^4 + x^3*(1+x)^9 + x^4*(1+x)^16 + x^5*(1+x)^25 + x^6*(1+x)^36 + x^7*(1+x)^49 + ... + x^n*(1+x)^(n^2) + ...
where
B(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 57*x^5 + 231*x^6 + 1023*x^7 + 4926*x^8 + 25483*x^9 + 140601*x^10 + ... + A121689(n)*x^n + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = -polcoeff( sum(m=0, #A, x^(m^2)*Ser(A)^m - x^m*(1+x +x*O(x^#A) )^(m^2) ), #A) ); A[n+1]}
for(n=0, 35, print1(a(n), ", "))

Crossrefs

Cf. A325298, A121689.

Sequence in context: A120567 A263779 A328432 * A125280 A338728 A022493

Adjacent sequences: A337847 A337848 A337849 * A337851 A337852 A337853

Keyword

nonn

Author

Paul D. Hanna, Sep 26 2020

Status

approved