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%I #17 Mar 28 2022 15:08:42
%S 1,3,4,11,33,114,445,1923,9078,46369,254297,1487896,9239135,60615819,
%T 418583924,3032405831,22979752405,181697363626,1495586215841,
%U 12789423056183,113415288869750,1041244540823413,9881851825756365,96811870321650792,977851660102425867
%N a(n) = 2*A040027(n-1) + Bell(n), where Bell = A000110.
%H H. W. Gould & J. Quaintance, <a href="https://doi.org/10.2298/AADM0702371G">A linear binomial recurrence and the Bell numbers and polynomials</a>, Applic. Anal. Discr. Math 1 (2007) 371-385.
%F a(0) = 1, a(1) = 3; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * a(n-k). - _Ilya Gutkovskiy_, Jul 10 2020
%p A038559 := proc(n)
%p 2*A040027(n-1)+combinat[bell](n) ;
%p end proc: # _R. J. Mathar_, Dec 20 2013
%p alias(PS = ListTools:-PartialSums):
%p A038559List := proc(len) local a, k, P, T; a := 3; P := [1]; T := [1];
%p for k from 1 to len-1 do
%p T := [op(T), a]; P := PS([a, op(P)]); a := P[-1] od;
%p T end: A038559List(25); # _Peter Luschny_, Mar 28 2022
%Y Cf. A000110, A040027.
%K easy,nonn
%O 0,2
%A _Henry Gould_
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