A340935 G.f. A(x) satisfies: A(x) = Sum_{n>=0} x^n/(1 - x*A(x)^(2*n)).

1, 2, 3, 8, 31, 146, 754, 4168, 24387, 149878, 961735, 6413730, 44305495, 316289264, 2329690081, 17685913364, 138276568051, 1112831978494, 9214885055084, 78482008660596, 687242245179732, 6184901074959982, 57179080181866903, 542740440965244192

Offset

0,2

Comments

Equals row sums of triangle A340934.

Links

Table of n, a(n) for n=0..23.

Example

G.f.: A(x) = 1 + 2*x + 3*x^2 + 8*x^3 + 31*x^4 + 146*x^5 + 754*x^6 + 4168*x^7 + 24387*x^8 + 149878*x^9 + 961735*x^10 + 6413730*x^11 + 44305495*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^(2*m) +x*O(x^n))) ); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A340934.

Sequence in context: A072042 A372711 A160586 * A162074 A162052 A082569

Adjacent sequences: A340932 A340933 A340934 * A340936 A340937 A340938

Keyword

nonn

Author

Paul D. Hanna, Jan 28 2021

Status

approved