A353831 Product_{n>=1} (1 + a(n)*x^n) = Sum_{n>=0} Bell(n)*x^n, where Bell = A000110.

1, 2, 3, 12, 34, 139, 610, 3046, 15604, 88460, 526274, 3344037, 22270254, 156359026, 1146627256, 8796070308, 70227355786, 583404596184, 5027823752930, 44907492540298, 414877525216196, 3960083715148092, 38996757506464858, 395754951565246801, 4134132167169618654, 44409616948511664062

Offset: 1

Author

Ilya Gutkovskiy, May 11 2022

Keywords

• nonn

Crossrefs

Cf. A000110, A085686, A157161, A305846.

Programs

Mathematica

A[m_, n_] := A[m, n] = Which[m == 1, BellB[n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 26]