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

Author

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

Keywords

• nonn

Examples

			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.
		

Links

• 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.

Programs

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 *)