OFFSET

0,4

COMMENTS

This is the triangle of denominators from Leibniz's harmonic triangle, A003506, augmented with a main diagonal of 0's.

Note, the usual definition of the exponential Riordan array [f(x), x*g(x)] associated with a pair of power series f(x) and g(x) requires f(0) to be nonzero. Here we don't make this assumption. - Peter Bala, Feb 13 2017

FORMULA

T(n,k) = (n-k)*binomial(n,k) for 0 <= k <= n.

E.g.f.: x*exp(x)*exp(x*t) = 1 + x + (2 + 2*t)*x^2/2! + (3 + 6*t + 3*t^2)*x^3/3! + ....

EXAMPLE

Triangle begins

.n\k.|..0.....1.....2.....3.....4.....5.....6

= = = = = = = = = = = = = = = = = = = = = = =

..0..|..0

..1..|..1.....0

..2..|..2.....2.....0

..3..|..3.....6.....3.....0

..4..|..4....12....12.....4.....0

..5..|..5....20....30....20.....5.....0

..6..|..6....30....60....60....30.....6.....0

...

MAPLE

A216973_row := proc(n) x*exp(x)*exp(x*t): series(%, x, n+1): n!*coeff(%, x, n):

seq(coeff(%, t, k), k=0..n) end:

for n from 0 to 10 do A216973_row(n) od; # Peter Luschny, Feb 03 2017

MATHEMATICA

(* The function RiordanArray is defined in A256893. *)

RiordanArray[# Exp[#]&, Identity, 11, True] // Flatten (* Jean-François Alcover, Jul 16 2019 *)

CROSSREFS

KEYWORD

AUTHOR

Peter Bala, Sep 21 2012

STATUS

approved