A273957 G.f. A(x) satisfies: A(x - x/(1+x)*A(x)) = x.

1, 1, 2, 7, 31, 159, 909, 5657, 37750, 267367, 1995167, 15601743, 127317160, 1080705251, 9517003663, 86763537749, 817415449402, 7946161682759, 79599437483758, 820726329776013, 8701095694308761, 94761241694697957, 1059246307095497960, 12143075480602664161, 142660989450995958519, 1716427548002953822635, 21135147232385131769271

Offset

1,3

Links

Table of n, a(n) for n=1..27.

Formula

G.f. A(x) satisfies:

(1) A(x) = x + Sum_{n>=1} (d/dx)^(n-1) ( x/(1+x)*A(x) )^n / n!.

(2) A(x) = x * exp( Sum_{n>=1} (d/dx)^(n-1) (1/x) * ( x/(1+x)*A(x) )^n / n! ).

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 31*x^5 + 159*x^6 + 909*x^7 + 5657*x^8 + 37750*x^9 + 267367*x^10 + 1995167*x^11 + 15601743*x^12 +...

Prog

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

Crossrefs

Sequence in context: A107595 A193320 A030882 * A221958 A221957 A030966

Adjacent sequences: A273954 A273955 A273956 * A273958 A273959 A273960

Keyword

nonn

Author

Paul D. Hanna, Jun 10 2016

Status

approved