A102289 Total number of odd lists in all sets of lists, cf. A000262.

0, 1, 2, 15, 76, 665, 5286, 56287, 597080, 7601841, 99702730, 1484554511, 23049638052, 393702612745, 7036703742446, 135702811542495, 2737989749177776, 58848546456947297, 1321063959370833810, 31310238786268648591, 773291778432688011260, 20031956775840631151481

Offset

0,3

Links

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

Formula

E.g.f.: x/(1-x^2)*exp(x/(1-x)).

a(n) = n*a(n-1) + n^2*a(n-2) - (n-2)^2*n*a(n-3). - Vaclav Kotesovec, Sep 29 2013

a(n) ~ sqrt(2)/4 * n^(n+1/4)*exp(2*sqrt(n)-n-1/2) * (1 + 7/(48*sqrt(n))). - Vaclav Kotesovec, Sep 29 2013

Maple

G:=(x/(1-x^2))*exp(x/(1-x)): Gser:=series(G, x=0, 25): seq(n!*coeff(Gser, x^n), n=1..22); # Emeric Deutsch
# second Maple program:
b:= proc(n) option remember; `if`(n=0, [1, 0], add(
      (p-> p+`if`(j::odd, [0, p[1]], 0))(b(n-j)*
        binomial(n-1, j-1)*j!), j=1..n))
    end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..25);  # Alois P. Heinz, May 10 2016

Mathematica

Rest[CoefficientList[Series[x/(1-x^2)*E^(x/(1-x)), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Sep 29 2013 *)
nxt[{n_, a_, b_, c_}]:={n+1, b, c, (n+1)*c+(n+1)^2*b-(n-1)^2 (n+1)*a}; NestList[ nxt, {2, 0, 1, 2}, 30][[All, 2]] (* Harvey P. Dale, Jan 13 2019 *)

Crossrefs

Cf. A052852, A066897, A066898, A059570, A059570, A081358, A092691.

Sequence in context: A099743 A283842 A344215 * A041243 A216247 A291972

Adjacent sequences: A102286 A102287 A102288 * A102290 A102291 A102292

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 19 2005

Extensions

More terms from Emeric Deutsch, Jun 24 2005

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

Status

approved