A301434 G.f. A(x) satisfies: A(x) = Sum_{n>=0} ((1+x)^n - 1)^n * A(x)^n.

1, 1, 5, 44, 515, 7475, 129525, 2619384, 60823498, 1600232884, 47150091652, 1539874276303, 55237696912990, 2159149195744518, 91335745732513695, 4156560037257263852, 202458583588324775958, 10507835578532315131098, 578860329653382364799458, 33730837645131194789676597, 2072763842696435360327368451, 133954882943472707055024904486, 9082145193772600621881071937985

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Example

G.f.: A(x) = 1 + x + 5*x^2 + 44*x^3 + 515*x^4 + 7475*x^5 + 129525*x^6 + 2619384*x^7 + 60823498*x^8 + 1600232884*x^9 + 47150091652*x^10 + ...
such that
A(x) = 1  +  ((1+x) - 1)*A(x)  +  ((1+x)^2 - 1)^2*A(x)^2  +  ((1+x)^3 - 1)^3*A(x)^3  +  ((1+x)^4 - 1)^4*A(x)^4  +  ((1+x)^5 - 1)^5*A(x)^5  + ...
Also,
A(x) = 1/(1 + A(x))  +  A(x)*(1+x)/(1 + (1+x)*A(x))^2  +  A(x)^2*(1+x)^4/(1 + (1+x)^2*A(x))^3  +  A(x)^3*(1+x)^9/(1 + (1+x)^3*A(x))^4  +  A(x)^4*(1+x)^16/(1 + (1+x)^4*A(x))^5  + ...

Prog

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

Crossrefs

Cf. A301433.

Sequence in context: A054766 A369216 A252830 * A232192 A249791 A215648

Adjacent sequences: A301431 A301432 A301433 * A301435 A301436 A301437

Keyword

nonn

Author

Paul D. Hanna, Mar 25 2018

Status

approved