A353944 Product_{n>=1} 1 / (1 - a(n)*x^n) = Sum_{n>=0} Bell(n)*x^n, where Bell = A000110.
1, 1, 3, 9, 34, 132, 610, 2929, 15604, 87310, 526274, 3325946, 22270254, 155986944, 1146627256, 8787134873, 70227355786, 583161239732, 5027823752930, 44899767806134, 414877525216196, 3959806750825202, 38996757506464858, 395743830189684984, 4134132167169618654, 44409120984298440176
Offset: 1
Keywords
Programs
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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 - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 26]
Formula
Conjecture: a(n) ~ Bell(n). - Vaclav Kotesovec, May 12 2022