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A111413 a(n) = f(f(n+1))-f(f(n)), where f(m) = Euler(m) = A000111(m).

%I A111413 #12 Apr 25 2022 08:21:20
%S A111413 0,0,0,15,19391512129,
%T A111413 703237958001393736999896827714634659411015090272684227831001142371615151
%N A111413 a(n) = f(f(n+1))-f(f(n)), where f(m) = Euler(m) = A000111(m).
%H A111413 Alois P. Heinz, <a href="/A111413/b111413.txt">Table of n, a(n) for n = 0..6</a>
%p A111413 b:= proc(u, o) option remember;
%p A111413       `if`(u+o=0, 1, add(b(o-1+j, u-j), j=1..u))
%p A111413     end:
%p A111413 a:= n-> (f-> f(f(n+1))-f(f(n)))(k-> b(k, 0)):
%p A111413 seq(a(n), n=0..5);  # _Alois P. Heinz_, Aug 17 2021
%t A111413 $RecursionLimit = Infinity;
%t A111413 t[n_, 0] := Boole[n == 0];
%t A111413 t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k];
%t A111413 f[n_] := t[n, n];
%t A111413 a[n_] := f[f[n+1]] - f[f[n]];
%t A111413 Table[a[n], {n, 0, 5}] (* _Jean-François Alcover_, Apr 25 2022 *)
%Y A111413 Cf. A000111.
%K A111413 nonn
%O A111413 0,4
%A A111413 _N. J. A. Sloane_, Nov 12 2005
%E A111413 Definition corrected by _N. J. A. Sloane_, Feb 14 2018