A340892 G.f. A(x) satisfies: A(x) = (1 - x*A(x)) * Sum_{n>=0} x^n*A(x)^n / (1 - x*A(x)^(n+1)).

1, 1, 2, 6, 22, 90, 394, 1807, 8577, 41810, 208218, 1055418, 5429926, 28294906, 149091449, 793344134, 4258741610, 23043290306, 125589061313, 689061968319, 3804200404388, 21125338986694, 117963378773322, 662200103423786, 3736364727815999, 21186955753874840

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 22*x^4 + 90*x^5 + 394*x^6 + 1807*x^7 + 8577*x^8 + 41810*x^9 + 208218*x^10 + 1055418*x^11 + 5429926*x^12 + ...
where
A(x)/(1 - x*A(x))  =  1/(1 - x*A(x)) + x*A(x)/(1 - x*A(x)^2) + x^2*A(x)^2/(1 - x*A(x)^3) + x^3*A(x)^3/(1 - x*A(x)^4) + x^4*A(x)^4/(1 - x*A(x)^5) + ...

Prog

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

Crossrefs

Cf. A340361, A340891.

Sequence in context: A155069 A006318 A103137 * A165546 A279568 A053617

Adjacent sequences: A340889 A340890 A340891 * A340893 A340894 A340895

Keyword

nonn

Author

Paul D. Hanna, Jan 25 2021

Status

approved