A340911 G.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n/(1 - x*A(x)^n).

1, 2, 3, 6, 16, 52, 189, 740, 3067, 13330, 60366, 283504, 1376000, 6884364, 35440060, 187471028, 1018049493, 5671511886, 32396788157, 189673021414, 1137795705447, 6991058047594, 43984892028735, 283267507353084, 1866622184589906

Offset

0,2

Comments

Equals row sums of triangle A340910.

Links

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

Example

G.f.: A(x) = 1 + 2*x + 3*x^2 + 6*x^3 + 16*x^4 + 52*x^5 + 189*x^6 + 740*x^7 + 3067*x^8 + 13330*x^9 + 60366*x^10 + 283504*x^11 + 1376000*x^12 + ...
where
A(x) = 1/(1-x) + x/(1 - x*A(x)) + x^2/(1 - x*A(x)^2) + x^3/(1 - x*A(x)^3) + x^4/(1 - x*A(x)^4) + x^5/(1 - x*A(x)^5) + ...

Prog

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

Crossrefs

Cf. A340910.

Sequence in context: A145860 A305190 A087983 * A328409 A103593 A174118

Adjacent sequences: A340908 A340909 A340910 * A340912 A340913 A340914

Keyword

nonn

Author

Paul D. Hanna, Jan 26 2021

Status

approved