cp's OEIS Frontend

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

%I A102289 #14 Jan 13 2019 13:46:07
%S A102289 0,1,2,15,76,665,5286,56287,597080,7601841,99702730,1484554511,
%T A102289 23049638052,393702612745,7036703742446,135702811542495,
%U A102289 2737989749177776,58848546456947297,1321063959370833810,31310238786268648591,773291778432688011260,20031956775840631151481
%N A102289 Total number of odd lists in all sets of lists, cf. A000262.
%H A102289 Alois P. Heinz, <a href="/A102289/b102289.txt">Table of n, a(n) for n = 0..444</a>
%F A102289 E.g.f.: x/(1-x^2)*exp(x/(1-x)).
%F A102289 a(n) = n*a(n-1) + n^2*a(n-2) - (n-2)^2*n*a(n-3). - _Vaclav Kotesovec_, Sep 29 2013
%F A102289 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
%p A102289 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_
%p A102289 # second Maple program:
%p A102289 b:= proc(n) option remember; `if`(n=0, [1, 0], add(
%p A102289       (p-> p+`if`(j::odd, [0, p[1]], 0))(b(n-j)*
%p A102289         binomial(n-1, j-1)*j!), j=1..n))
%p A102289     end:
%p A102289 a:= n-> b(n, 0)[2]:
%p A102289 seq(a(n), n=0..25);  # _Alois P. Heinz_, May 10 2016
%t A102289 Rest[CoefficientList[Series[x/(1-x^2)*E^(x/(1-x)), {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Sep 29 2013 *)
%t A102289 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 *)
%Y A102289 Cf. A052852, A066897, A066898, A059570, A059570, A081358, A092691.
%K A102289 easy,nonn
%O A102289 0,3
%A A102289 _Vladeta Jovovic_, Feb 19 2005
%E A102289 More terms from _Emeric Deutsch_, Jun 24 2005
%E A102289 a(0)=0 pepended by _Alois P. Heinz_, May 10 2016