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A173109 Row sums of triangle A173108.

%I A173109 #26 Apr 22 2022 09:12:17
%S A173109 1,1,3,6,18,58,221,935,4361,22082,120336,700652,4333933,28345089,
%T A173109 195233255,1411303634,10675375402,84276173438,692752181561,
%U A173109 5917018378495,52416910416933,480786834535246,4559132648864256,44632792689619592,450518001943669545
%N A173109 Row sums of triangle A173108.
%H A173109 Alois P. Heinz, <a href="/A173109/b173109.txt">Table of n, a(n) for n = 0..576</a>
%F A173109 G.f.: G(0)/(1-x^2)/(1+x) where G(k) =  1 - 2*x*(k+1)/((2*k+1)*(2*x*k-1) - x*(2*k+1)*(2*k+3)*(2*x*k-1)/(x*(2*k+3) - 2*(k+1)*(2*x*k+x-1)/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Jan 04 2013.
%F A173109 G.f.: ( G(0) - 1 )/(1-x^2) where G(k) =  1 + (1-x)/(1-x*k)/(1-x/(x+(1-x)/G(k+1) )); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Jan 22 2013
%F A173109 a(n+1) - a(n) = A087650(n+1). - _Vladimir Reshetnikov_, Oct 29 2015
%F A173109 a(n) = Sum_{k=0..floor(n/2)} A000110(n-2*k). - _Alois P. Heinz_, Jun 17 2021
%e A173109 a(5) = 58 = 52 + 5 + 1.
%p A173109 b:= proc(n) option remember; `if`(n=0, 1,
%p A173109       add(b(n-j)*binomial(n-1, j-1), j=1..n))
%p A173109     end:
%p A173109 a:= n-> add(b(n-2*k), k=0..iquo(n, 2)):
%p A173109 seq(a(n), n=0..25);  # _Alois P. Heinz_, Jun 17 2021
%t A173109 a[n_] := Sum[BellB[n-2k], {k, 0, Quotient[n, 2]}];
%t A173109 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 22 2022 *)
%Y A173109 Cf. A000110, A087650, A173108.
%K A173109 nonn
%O A173109 0,3
%A A173109 _Gary W. Adamson_, Feb 09 2010
%E A173109 More terms from _Sergei N. Gladkovskii_, Jan 04 2013