OFFSET
5,1
COMMENTS
Generalizes Stirling numbers of the first kind.
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 257.
LINKS
Alois P. Heinz, Rows n = 5..300, flattened
Eric Weisstein's World of Mathematics, Permutation Cycle.
EXAMPLE
Triangle begins:
05: 24;
06: 120;
07: 720;
08: 5040;
09: 40320;
10: 362880, 72576;
11: 3628800, 1330560;
12: 39916800, 20338560;
MAPLE
b:= proc(n) option remember; expand(`if`(n=0, 1, add(
b(n-i)*x*binomial(n-1, i-1)*(i-1)!, i=5..n)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(b(n)):
seq(T(n), n=5..20); # Alois P. Heinz, Sep 25 2016
MATHEMATICA
b[n_] := b[n] = Expand[If[n == 0, 1, Sum[b[n - i]*x*Binomial[n - 1, i - 1]* (i - 1)!, {i, 5, n}]]];
T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, Exponent[p, x]}]][ b[n]];
T /@ Range[5, 20] // Flatten (* Jean-François Alcover, Dec 08 2019, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
Offset changed from 1 to 5 by Alois P. Heinz, Sep 25 2016
STATUS
approved