A111413 - OEIS

%I #12 Apr 25 2022 08:21:20

%S 0,0,0,15,19391512129,

%T 703237958001393736999896827714634659411015090272684227831001142371615151

%N a(n) = f(f(n+1))-f(f(n)), where f(m) = Euler(m) = A000111(m).

%H Alois P. Heinz, <a href="/A111413/b111413.txt">Table of n, a(n) for n = 0..6</a>

%p b:= proc(u, o) option remember;

%p       `if`(u+o=0, 1, add(b(o-1+j, u-j), j=1..u))

%p     end:

%p a:= n-> (f-> f(f(n+1))-f(f(n)))(k-> b(k, 0)):

%p seq(a(n), n=0..5);  # _Alois P. Heinz_, Aug 17 2021

%t $RecursionLimit = Infinity;

%t t[n_, 0] := Boole[n == 0];

%t t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k];

%t f[n_] := t[n, n];

%t a[n_] := f[f[n+1]] - f[f[n]];

%t Table[a[n], {n, 0, 5}] (* _Jean-François Alcover_, Apr 25 2022 *)

%Y Cf. A000111.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Nov 12 2005

%E Definition corrected by _N. J. A. Sloane_, Feb 14 2018