A220895 Number of closed lambda-terms of size n with at most 1 free de Bruijn index.

1, 3, 13, 76, 542, 4493, 42131, 439031, 5020105, 62382279, 835980065, 12004984120, 183754242626, 2984264710781, 51220227153987, 925859588215096, 17571969962025822, 349210371834021295, 7249185099929421649, 156847124089924073770, 3530125495029323284404

Offset: 0

Author

N. J. A. Sloane, Dec 31 2012

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Katarzyna Grygiel and Pierre Lescanne, Counting and generating lambda-terms, arXiv preprint arXiv:1210.2610 [cs.LO], 2012.

Programs

Mathematica

T[0, m_] := m; T[n_, m_] := T[n, m] = T[n-1, m+1] + Sum[T[i, m] T[n-i-1, m], {i, 0, n-1}];
a[n_] := T[n, 1];
Table[a[n], {n, 0, 14}] (* Jean-François Alcover, May 23 2017 *)

Formula

Grygiel and Lescanne give a recurrence.

Extensions

More terms from Alois P. Heinz, May 23 2017