A396645 a(n) = Sum_{j=1..n} |Stirling1(n-1,j-1)| * a(n-j) for n>=1, starting with a(0) = 1.

1, 1, 1, 2, 6, 30, 290, 5795, 273131, 33435365, 11684100029, 12420429123560, 42758167792063420, 497197306541110815666, 20499715659897938314285818, 3096905029809572116833551189888, 1787271136443917603307861222439598096, 4049832282285832299658439630909210798514596

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..59

Wikipedia, Stirling numbers of the first kind

Formula

a(n) = Sum_{j=1..n} A132393(n-1,j-1) * a(n-j) for n>=1, a(0) = 1.

Maple

b:= proc(n) option remember; expand(`if`(n=0, 1,
      add(b(n-j)*x*binomial(n-1, j-1)*(j-1)!, j=1..n)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-j)*coeff(b(n-1), x, j-1), j=1..n))
    end:
seq(a(n), n=0..17);

Crossrefs

Cf. A000110, A132393, A329968, A381515.

Sequence in context: A275593 A381377 A120295 * A071350 A324853 A329558

Adjacent sequences: A396642 A396643 A396644 * A396647 A396648 A396649

Keyword

nonn,new

Author

Alois P. Heinz, Jun 29 2026

Status

approved