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A088313 Number of "sets of lists" (cf. A000262) with an odd number of lists. 4
0, 1, 2, 7, 36, 241, 1950, 18271, 193256, 2270017, 29272410, 410815351, 6231230412, 101560835377, 1769925341366, 32838929702671, 646218442877520, 13441862819232001, 294656673023216946, 6788407001443004647, 163962850573039534580, 4142654439686285737201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..444

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.

N. J. A. Sloane, LAH transform

FORMULA

E.g.f.: sinh(x/(1-x)).

a(n) = Sum_{k=1.. floor((n+1)/2)} n!/(2*k-1)!*binomial(n-1, 2*k-2).

E.g.f.: sinh(x/(1-x)) = x/(2-2*x)*E(0), where E(k)= 1 + 1/( 1 - x^2/(x^2 + 2*(1-x)^2*(k+1)*(2*k+3)/E(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 16 2013

a(n) ~ 2^(-3/2) * n^(n-1/4) * exp(2*sqrt(n)-n-1/2). - Vaclav Kotesovec, Jul 04 2015

MAPLE

b:= proc(n, t) option remember; `if`(n=0, t, add(

      b(n-j, 1-t)*binomial(n-1, j-1)*j!, j=1..n))

    end:

a:= n-> b(n, 0):

seq(a(n), n=0..30);  # Alois P. Heinz, May 10 2016

MATHEMATICA

Rest[CoefficientList[Series[Sinh[x/(1-x)], {x, 0, 20}], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jul 04 2015 *)

PROG

(PARI) x='x+O('x^66); Vec(serlaplace(sinh(x/(1-x)))) \\ Joerg Arndt, Jul 16 2013

CROSSREFS

Cf. A000262, A027187, A024429, A024430, A001710, A109777, A088312.

Sequence in context: A119736 A308750 A088715 * A201197 A185754 A191493

Adjacent sequences:  A088310 A088311 A088312 * A088314 A088315 A088316

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Nov 05 2003

EXTENSIONS

a(0)=0 prepended by Alois P. Heinz, May 10 2016

STATUS

approved

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)