A109777 G.f. = f(x), where f(x)^2 = o.g.f. for A088313 (with offset 0).

1, 1, 3, 15, 101, 829, 7891, 84735, 1009065, 13170841, 186798003, 2859068831, 46960097413, 823787983021, 15370572776091, 303929827526887, 6348320745774993, 139663855708967665, 3227812335094695171, 78180132507785056399, 1980181972528939129861, 52344600987011191983613

Offset

0,3

Links

Table of n, a(n) for n=0..21.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Example

The present sequence has g.f. f(x) = 1 + x + 3*x^2 + 15*x^3 + ...
A088313 [1,2,7,36,242,...] has e.g.f. = sinh(x/(1-x)) = x + x^2 + 7/6*x^3 + 3/2*x^4 + 241/120*x^5 + 65/24*x^6 + 18271/5040*x^7 + ... and (with offset 0) o.g.f. = 1 + 2*x^2 + 7*x^3 + 36*x^4 + ... = f(x)^2.

Mathematica

nmax = 22;
f[x_] = Sqrt[Sum[SeriesCoefficient[Sinh[x/(1-x)], {x, 0, n}] n! x^n, {n, 0, nmax}]] + O[x]^nmax // Normal;
List @@ f[x] /. x -> 1 (* Jean-François Alcover, Oct 08 2018 *)

Crossrefs

Sequence in context: A074521 A074536 A152093 * A242003 A265164 A348793

Adjacent sequences: A109774 A109775 A109776 * A109778 A109779 A109780

Keyword

nonn

Author

N. J. A. Sloane and Nadia Heninger, Aug 15 2005

Status

approved