A220897 Number of closed lambda-terms of size n with at most 3 free de Bruijn indices.

3, 13, 99, 962, 10732, 131715, 1741813, 24537945, 365779679, 5744911157, 94786034723, 1639198623818, 29658034018852, 560484305049943, 11046637024014049, 226728682400563206, 4839249231632997924, 107262821628220974029, 2465723931357450572707

Offset: 0

Author

N. J. A. Sloane, Dec 31 2012

Keywords

• nonn

Links

• Katarzyna Grygiel and Pierre Lescanne, Counting and generating lambda-terms, arXiv preprint arXiv:1210.2610, 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, 3];
Table[a[n], {n, 0, 14}] (* Jean-François Alcover, May 23 2017 *)

Formula

Grygiel and Lescanne give a recurrence.