A229741 a(0)=1; thereafter a(n) = n! + Sum_{i=0..n-1} a(i)*a(n-1-i).

1, 2, 6, 22, 92, 428, 2208, 12756, 83848, 635392, 5563952, 55743168, 628294912, 7832530400, 106515280064, 1564127939088, 24618706734432, 413015301455040, 7352809011276096, 138398862650413248, 2745596388858393984, 57248882869605962880, 1251574614271552264704, 28625091198273426059136

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Stefan Forcey, Aaron Lauve and Frank Sottile, Cofree compositions of coalgebras, Annals of Combinatorics 17 (1) pp. 105-130 March, 2013.

Formula

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

Maple

a:= proc(n) option remember;
      `if`(n=0, 1, n! +add(a(i)*a(n-1-i), i=0..n-1))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Oct 10 2013

Mathematica

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 *)

Crossrefs

Cf. A260879.

Sequence in context: A074664 A367442 A091768 * A261518 A185349 A317652

Adjacent sequences: A229738 A229739 A229740 * A229742 A229743 A229744

Keyword

nonn

Author

N. J. A. Sloane, Oct 05 2013

Status

approved