A127681 a(0) = 1. a(n+1) = sum{k=0 to n} a(n-k)*a(ceiling(k/2)).

1, 1, 2, 4, 9, 19, 42, 90, 198, 428, 936, 2030, 4430, 9626, 20978, 45622, 99367, 216197, 470736, 1024420, 2230183, 4853881, 10566170, 22997974, 50061240, 108964596, 237186018, 516272178, 1123772192, 2446081048, 5324371354, 11589437278

Offset: 0

Author

Leroy Quet, Jan 23 2007

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..2958

Crossrefs

Cf. A127680.

Programs

Maple

f:= proc(n) option remember;
    add(procname(n-1-k)*procname(ceil(k/2)),k=0..n-1)
end proc:
f(0):= 1:
map(f, [$0..40]); # Robert Israel, Feb 16 2018

Mathematica

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 *)

Formula

a(n) ~ c * d^n, where d = 2.17668434612191638687360948440303534082431658053308188275404767951385648... and c = 0.39120452795484998747876543545867360129596245925827624710922741574667... - Vaclav Kotesovec, Nov 16 2021

Extensions

Extended by Ray Chandler, Feb 13 2007