A144011 E.g.f. satisfies: A'(x) = 1/(1 - x*A(x))^2 with A(0)=1.

1, 1, 2, 10, 72, 704, 8640, 127968, 2220288, 44179200, 991802880, 24799656960, 683533762560, 20589288993792, 672920058230784, 23717386619136000, 896730039462297600, 36203980633475973120, 1554541449858851143680

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..335

V. Kotesovec, Asymptotic of implicit functions if Fww = 0

Formula

E.g.f. A(x) satisfies: A(x) = 1 + Integral 1/(1 - x*A(x))^2 dx.

E.g.f. A(x) satisfies: x/(x*A(x)-1) = tan(1-A(x)). - Vaclav Kotesovec, Jun 15 2013

a(n) ~ GAMMA(1/3) * n^(n-5/6) * (2+Pi)^(n+1/3) / (3^(1/6) * sqrt(Pi) * exp(n) * 2^(n+5/6)). - Vaclav Kotesovec, Feb 23 2014

Mathematica

nn=10; Flatten[{1, Table[Subscript[c, j]*j!, {j, 1, nn}]/.Solve[Table[SeriesCoefficient[x/(x*(1+Sum[Subscript[c, j]*x^j, {j, 1, nn}])-1), {x, 0, k}]==SeriesCoefficient[Tan[-Sum[Subscript[c, j]*x^j, {j, 1, nn}]], {x, 0, k}], {k, 0, nn}]]}] (* Vaclav Kotesovec, Jun 15 2013 *)

Prog

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(1/(1-x*A+x*O(x^n))^2 )); n!*polcoeff(A, n)}

Crossrefs

Cf. A144010, A238302.

Sequence in context: A052555 A204808 A084844 * A238085 A277502 A231039

Adjacent sequences: A144008 A144009 A144010 * A144012 A144013 A144014

Keyword

nonn,nice

Author

Paul D. Hanna, Sep 10 2008

Status

approved