A193296 G.f. satisfies: A(x) = 1+x + x^2*A( (A(x)-1-x)/x ).

1, 1, 1, 1, 2, 5, 15, 51, 191, 773, 3338, 15243, 73131, 366815, 1916260, 10394665, 58404853, 339223859, 2033188222, 12556915219, 79807729238, 521399203037, 3497978659977, 24076009827669, 169865542733652, 1227553152971419, 9079751310622581

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..280

Formula

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

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

a(n) = [x^(n-2)] A(x)^(n-1)/(n-1) for n>=2 with a(0)=a(1)=1.

Example

G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 5*x^5 + 15*x^6 + 51*x^7 +...
where
(A(x)-1-x)/x = x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 51*x^6 + 191*x^7 +...
A((A(x)-1-x)/x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 51*x^5 + 191*x^6 +...
A(x)*A(x/A(x)) = 1 + 2*x + 2*x^2 + x^3 + 2*x^4 + 5*x^5 + 15*x^6 + 51*x^7 +...

Prog

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

Crossrefs

Sequence in context: A279556 A108307 A275605 * A304454 A287253 A117426

Adjacent sequences: A193293 A193294 A193295 * A193297 A193298 A193299

Keyword

nonn

Author

Paul D. Hanna, Jul 21 2011

Status

approved