%I
%S 1,1,3,7,29,129,757,5185,41155,368351,3671635,40295943,482758111,
%T 6268066531,87668492115,1314023850727,21011431917453,357014074280785,
%U 6423561495057421,122004755658629081,2439367774898883497,51213663674167659301,1126452985959434543237
%N First column of the matrix power A173279(.,.)^j in the limit j>infinity.
%C We can generalize A173279 to other matrices derived from some sequence S by Smat(n,k) := S(nr*k), r >= 2,
%C and find that they define sequences B(x) via S(x)= B(X)/B(x^r), b(n) = Sum_{t=0..n, nt == 0 (mod r)} S(t)*B_{(nt)/r}.
%C The sequence here is the case of S=A000142 and r=2.
%F A000142(x) = A(x)/A(x^2), where A(x) and A000142(x) are the o.g.f.'s associated with A000142 and this sequence here.
%F Sum_{n>=0} 1/a(n) = 2.519966353393413186683398448854995831308...
%F a(n) = (A173279^j)(n,0).
%F a(n) = Sum_{t=0..n, nt even} t!*a_{(nt)/2}.  _R. J. Mathar_, Feb 22 2010
%p A173280 := proc(n) option remember; local a,l; if n = 0 then 1; else a :=0 ; for l from n to 0 by 2 do a := a+ l!*procname((nl)/2) : end do ; a ; end if; end proc:
%p seq(A173280(n),n=0..60) ; # _R. J. Mathar_, Feb 22 2010
%Y Cf. A000142.
%K nonn
%O 0,3
%A _Gary W. Adamson_, Feb 14 2010
%E Extended, and invalid comment on convergence to e removed, by _R. J. Mathar_, Feb 22 2010
%E Index of B in the convolution formula in the comment corrected by _R. J. Mathar_, Mar 23 2010
