OFFSET
1,3
COMMENTS
FORMULA
T(n, k) = Sum_{i=0..k-1} |stirling1(n, n-i)| for 1 <= k <= n.
From Peter Bala, Jul 08 2012: (Start)
E.g.f.: x/(1-x)*{1/(1-x*z)^(1/x) - 1/(1-x*z)} = x*z + (x + 2*x^2)*z^2/2! + (x + 4*x^2 + 6*x^3)*z^3/3! + ... Cf. the e.g.f. of A059518.
(End)
EXAMPLE
T(5,3) = 46 because 18 + 4*7 = 46.
Triangle begins:
Row 1: 1
Row 2: 1 2
Row 3: 1 4 6
Row 4: 1 7 18 24
Row 5: 1 11 46 96 120
Row 6: 1 16 101 326 600 720
Row 7: 1 22 197 932 2556 4320 5040
MAPLE
with(combinat): T:=(n, k)->add(abs(stirling1(n, n-i)), i=0..k-1): for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form T:=proc(n, k) if k=1 then 1 elif k=n then n! else T(n-1, k)+(n-1)*T(n-1, k-1) fi end: for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form. - Emeric Deutsch, Jul 03 2005
A109822_row := proc(n) local k, i;
add(add(abs(combinat[stirling1](n, n-i)), i=0..k)*x^(n-k-1), k=0..n-1);
seq(coeff(%, x, n-k), k=1..n) end:
seq(print(A109822_row(n)), n=1..7); # Peter Luschny, Sep 18 2011
MATHEMATICA
Table[Sum[Abs@ StirlingS1[n, n - i], {i, 0, k - 1}], {n, 10}, {k, n}] // Flatten (* Michael De Vlieger, Aug 17 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Jul 03 2005
STATUS
approved