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A088312 Number of sets of lists (cf. A000262) with even number of lists. 4
1, 0, 1, 6, 37, 260, 2101, 19362, 201097, 2326536, 29668681, 413257790, 6238931821, 101415565836, 1765092183037, 32734873484250, 644215775792401, 13404753632014352, 293976795292186897, 6775966692145553526, 163735077313046119861, 4138498600079573989140 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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.: cosh(x/(1-x)).

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

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

a(n+4) - 2*(2*n+5)*a(n+3) + (6*n^2+24*n+23)*a(n+2) - 2*(n+1)*(n+2)*(2*n+3)*a(n+1) + n*(n+1)^2*(n+2)*a(n) = 0. - Emanuele Munarini, Sep 03 2017

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, 1):

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

MATHEMATICA

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

Table[Sum[n!/(2*k)! Binomial[n - 1, 2*k - 1], {k, 0, Floor[n/2]}], {n, 0, 12}] (* Emanuele Munarini, Sep 03 2017 *)

CROSSREFS

Cf. A027187, A024429, A024430, A001710, A088313.

Sequence in context: A192238 A140712 A079751 * A012364 A012719 A300171

Adjacent sequences:  A088309 A088310 A088311 * A088313 A088314 A088315

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Nov 05 2003

EXTENSIONS

More terms from Vaclav Kotesovec, Jul 04 2015

a(0)-a(1) prepended by Alois P. Heinz, May 10 2016

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)