OFFSET
1,4
COMMENTS
Row sums = n!
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
FORMULA
E.g.f. for column k: 1/(1-x) - D(x)*Sum_{i=0..k-1} x^i/i! where D(x) is the e.g.f. for A000166.
T(n,k) = Sum_{i=k..n} C(n,i)*A000166(n-i). - Alois P. Heinz, Apr 22 2013
EXAMPLE
Triangle begins:
1;
1, 1;
4, 1, 1;
15, 7, 1, 1;
76, 31, 11, 1, 1;
455, 191, 56, 16, 1, 1;
3186, 1331, 407, 92, 22, 1, 1;
...
MAPLE
b:= proc(n) b(n):= `if`(n<2, 1-n, (n-1)*(b(n-1)+b(n-2))) end:
T:= (n, k)-> add(binomial(n, i)*b(n-i), i=k..n):
seq(seq(T(n, k), k=1..n), n=1..12); # Alois P. Heinz, Apr 22 2013
MATHEMATICA
f[list_] := Select[list, #>0&]; Map[f, Transpose[Table[nn=10; d=Exp[-x]/(1-x); p=1/(1-x); s=Sum[x^i/i!, {i, 0, n}]; Drop[Range[0, nn]! CoefficientList[Series[p-s d, {x, 0, nn}], x], 1], {n, 0, 9}]]]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Mar 03 2012
STATUS
approved