OFFSET
1,3
LINKS
D. H. Lehmer, Generalized Eulerian numbers, J. Combin. Theory Ser.A 32 (1982), no. 2, 195-215. MR0654621 (83k:10026).
FORMULA
From Peter Bala, Oct 27 2015: (Start)
O.g.f. of n-th row of square array: 1/(1 - x)^n * (x*d/dx)^n (log(1/(1 - x)), for n >= 1.
E.g.f. of square array: log((1 - x)/(1 - x*exp(t/(1 - x)))).
Read as a triangle: T(n,k) = Sum_{i = 1..k} binomial(n-i,k-i)*i^(n-k) for 1 <= k <= n.
n-th row polynomial of triangle: Sum_{i = 0..n-1} x^i*(x + i)^(n-i). (End)
EXAMPLE
MAPLE
A211235 := (n, k) -> add(binomial(n-i, k-i)*i^(n-k), i = 1 .. k): for n from 1 to 10 do seq(A211235(n, k), k = 1 .. n) end do; # Peter Bala, Oct 27 2015
MATHEMATICA
T[n_, k_] := Sum[Binomial[n-i, k-i] * i^(n-k), {i, 1, k}]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] //Flatten (* Amiram Eldar, Nov 30 2018 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Apr 05 2012
EXTENSIONS
Terms a(37)-a(55) added by Peter Bala, Oct 27 2015
STATUS
approved