A183607 G.f. satisfies: A(x) = 1/(1 - x - x*{d/dx x^2*A'(x)/A(x)}).

1, 1, 3, 20, 249, 5087, 155180, 6609730, 374548937, 27237010543, 2471980167855, 273862966795982, 36371476538686396, 5704018487197135820, 1042929404101002643300, 219905097318369791869794, 52967138256595856156574553, 14453277961440111342752817767

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Formula

G.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where G(x) = A(x/G(x)) is the g.f. of A183606 and satisfies: [x^(n+1)] G(x)^n = n*(n+1)*{[x^n] G(x)^n} for n>=0.

G.f. A(x) satisfies: [x^n] exp( n * (x + x^2*A(x)'/A(x)) ) / A(x) = 0 for n > 0. - Paul D. Hanna, Oct 21 2020

a(n) ~ c * n! * (n-1)!, where c = 2.0524259870985684724972435... - Vaclav Kotesovec, Aug 24 2017

Example

G.f.: A(x) = 1 + x + 3*x^2 + 20*x^3 + 249*x^4 + 5087*x^5 + 155180*x^6 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/(1-x - x*deriv(x^2*A'/(A+x*O(x^n))))); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A183606.

Sequence in context: A349928 A262208 A324955 * A331504 A197322 A197975

Adjacent sequences: A183604 A183605 A183606 * A183608 A183609 A183610

Keyword

nonn

Author

Paul D. Hanna, Aug 11 2012

Status

approved