A302061 G.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n * (A(x) + (1+x)^n)^n.

1, 2, 7, 31, 155, 837, 4782, 28532, 176449, 1125498, 7382239, 49700694, 343141590, 2428982923, 17633960882, 131388799369, 1005725945342, 7917873364956, 64186727511015, 536333892783678, 4622903357471425, 41121524951530554, 377494322217082646, 3575008669714680175, 34902356546235071687

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

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

Example

G.f.: A(x) = 1 + 2*x + 7*x^2 + 31*x^3 + 155*x^4 + 837*x^5 + 4782*x^6 + 28532*x^7 + 176449*x^8 + 1125498*x^9 + 7382239*x^10 + ...
such that
A(x) = 1 + x*(A(x) + (1+x)) + x^2*(A(x) + (1+x)^2)^2 + x^3*(A(x) + (1+x)^3)^3 + x^4*(A(x) + (1+x)^4)^4 + x^5*(A(x) + (1+x)^5)^5 + x^6*(A(x) + (1+x)^6)^6 + ...
Also,
A(x) = 1/(1-x*A(x))  +  x*(1+x)/(1 - x*A(x)*(1+x))^2  +  x^2*(1+x)^4/(1 - x*A(x)*(1+x)^2)^3  +  x^3*(1+x)^9/(1 - x*A(x)*(1+x)^3)^4  +  x^4*(1+x)^16/(1 - x*A(x)*(1+x)^4)^5  +  x^5*(1+x)^25/(1 - x*A(x)*(1+x)^5)^6  ...

Prog

(PARI) {a(n) = my(A=1); for(i=1, n, A = sum(m=0, n, x^m * (A + (1+x +x*O(x^n))^m)^m ) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A301433.

Sequence in context: A368931 A007863 A369214 * A030823 A030873 A030913

Adjacent sequences: A302058 A302059 A302060 * A302062 A302063 A302064

Keyword

nonn

Author

Paul D. Hanna, Apr 07 2018

Status

approved