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a(1) = 1; a(n) = Sum_{k=1..ceiling(n/2)} a(k) * a(n-k).
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%I #8 Nov 04 2021 18:38:18

%S 1,1,2,3,7,14,33,70,173,400,1008,2391,6132,15019,38799,96520,252022,

%T 638788,1679091,4297452,11373921,29426350,78204705,203658812,

%U 543828898,1426912159,3822817135,10078227662,27092960887,71803114869,193496832857,514684042158

%N a(1) = 1; a(n) = Sum_{k=1..ceiling(n/2)} a(k) * a(n-k).

%H Alois P. Heinz, <a href="/A348530/b348530.txt">Table of n, a(n) for n = 1..2238</a>

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

%p add(a(k)*a(n-k), k=1..ceil(n/2)))

%p end:

%p seq(a(n), n=1..32); # _Alois P. Heinz_, Oct 21 2021

%t a[1] = 1; a[n_] := a[n] = Sum[a[k] a[n - k], {k, 1, Ceiling[n/2]}]; Table[a[n], {n, 1, 32}]

%Y Cf. A000108, A000992.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Oct 21 2021