A229189 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^n * Product_{k=1..n} (A(x)^k - x^k).

1, 1, 2, 9, 44, 239, 1375, 8263, 51357, 327693, 2135950, 14170571, 95427286, 650944504, 4490552235, 31288674796, 219971575861, 1559144159064, 11134345158295, 80071382287309, 579625552498596, 4222207701924925, 30942404146965589, 228099487538025285, 1691276257040925428

Offset

0,3

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 9*x^3 + 44*x^4 + 239*x^5 + 1375*x^6 + 8263*x^7 +...
where g.f. A = A(x) satisfies:
A(x) = 1 + x*A*(A-x) + x^2*A^2*(A-x)*(A^2-x^2) + x^3*A^3*(A-x)*(A^2-x^2)*(A^3-x^3) + x^4*A^4*(A-x)*(A^2-x^2)*(A^3-x^3)*(A^4-x^4) + x^5*A^5*(A-x)*(A^2-x^2)*(A^3-x^3)*(A^4-x^4)*(A^5-x^5) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*A^m*prod(k=1, m, A^k-x^k +x*O(x^n)))); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A229182.

Sequence in context: A124889 A317134 A295809 * A365129 A371576 A246812

Adjacent sequences: A229186 A229187 A229188 * A229190 A229191 A229192

Keyword

nonn

Author

Paul D. Hanna, Sep 15 2013

Status

approved