%I #26 Apr 22 2022 09:12:17

%S 1,1,3,6,18,58,221,935,4361,22082,120336,700652,4333933,28345089,

%T 195233255,1411303634,10675375402,84276173438,692752181561,

%U 5917018378495,52416910416933,480786834535246,4559132648864256,44632792689619592,450518001943669545

%N Row sums of triangle A173108.

%H Alois P. Heinz, <a href="/A173109/b173109.txt">Table of n, a(n) for n = 0..576</a>

%F 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 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 a(n+1) - a(n) = A087650(n+1). - _Vladimir Reshetnikov_, Oct 29 2015

%F a(n) = Sum_{k=0..floor(n/2)} A000110(n-2*k). - _Alois P. Heinz_, Jun 17 2021

%e a(5) = 58 = 52 + 5 + 1.

%p b:= proc(n) option remember; `if`(n=0, 1,

%p add(b(n-j)*binomial(n-1, j-1), j=1..n))

%p end:

%p a:= n-> add(b(n-2*k), k=0..iquo(n, 2)):

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Jun 17 2021

%t a[n_] := Sum[BellB[n-2k], {k, 0, Quotient[n, 2]}];

%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 22 2022 *)

%Y Cf. A000110, A087650, A173108.

%K nonn

%O 0,3

%A _Gary W. Adamson_, Feb 09 2010

%E More terms from _Sergei N. Gladkovskii_, Jan 04 2013