A127681 - OEIS

%I #14 Nov 16 2021 03:42:16

%S 1,1,2,4,9,19,42,90,198,428,936,2030,4430,9626,20978,45622,99367,

%T 216197,470736,1024420,2230183,4853881,10566170,22997974,50061240,

%U 108964596,237186018,516272178,1123772192,2446081048,5324371354,11589437278

%N a(0) = 1. a(n+1) = sum{k=0 to n} a(n-k)*a(ceiling(k/2)).

%H Robert Israel, <a href="/A127681/b127681.txt">Table of n, a(n) for n = 0..2958</a>

%F a(n) ~ c * d^n, where d = 2.17668434612191638687360948440303534082431658053308188275404767951385648... and c = 0.39120452795484998747876543545867360129596245925827624710922741574667... - _Vaclav Kotesovec_, Nov 16 2021

%p f:= proc(n) option remember;

%p     add(procname(n-1-k)*procname(ceil(k/2)),k=0..n-1)

%p end proc:

%p f(0):= 1:

%p map(f, [$0..40]); # _Robert Israel_, Feb 16 2018

%t f[l_List] := Block[{n = Length[l] - 1},Append[l, Sum[l[[n - k + 1]]*l[[Ceiling[k/2] + 1]], {k, 0, n}]]];Nest[f, {1}, 32] (* _Ray Chandler_, Feb 13 2007 *)

%Y Cf. A127680.

%K easy,nonn

%O 0,3

%A _Leroy Quet_, Jan 23 2007

%E Extended by _Ray Chandler_, Feb 13 2007