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a(0)=1; thereafter a(n) = n! + Sum_{i=0..n-1} a(i)*a(n-1-i).
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%I #16 Aug 02 2015 06:12:54

%S 1,2,6,22,92,428,2208,12756,83848,635392,5563952,55743168,628294912,

%T 7832530400,106515280064,1564127939088,24618706734432,413015301455040,

%U 7352809011276096,138398862650413248,2745596388858393984,57248882869605962880,1251574614271552264704,28625091198273426059136

%N a(0)=1; thereafter a(n) = n! + Sum_{i=0..n-1} a(i)*a(n-1-i).

%H Alois P. Heinz, <a href="/A229741/b229741.txt">Table of n, a(n) for n = 0..300</a>

%H Stefan Forcey, Aaron Lauve and Frank Sottile, <a href="http://dx.doi.org/10.1007/s00026-012-0170-5">Cofree compositions of coalgebras</a>, Annals of Combinatorics 17 (1) pp. 105-130 March, 2013.

%F a(n) ~ n! * (1 + 2/n + 8/n^2 + 44/n^3 + 288/n^4 + 2148/n^5 + 17816/n^6 + 161852/n^7 + 1594280/n^8 + 16911940/n^9 + 192361656/n^10), for coefficients see A260879. - _Vaclav Kotesovec_, Aug 02 2015

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

%p `if`(n=0, 1, n! +add(a(i)*a(n-1-i), i=0..n-1))

%p end:

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Oct 10 2013

%t a[0] = 1; a[n_] := a[n] = n! + Sum[a[i]*a[n-1-i], {i, 0, n-1}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 07 2014 *)

%Y Cf. A260879.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 05 2013