A287697 Triangle read by rows, (Sum_{k=0..n} T[n,k]*x^k) / (1-x)^(n+1) are generating functions of the columns of A287698.

1, 0, 1, 0, 1, 7, 0, 1, 52, 163, 0, 1, 341, 4499, 8983, 0, 1, 2246, 98256, 660746, 966751, 0, 1, 15177, 2045282, 35677082, 155729277, 179781181, 0, 1, 104952, 42658239, 1754605504, 17446464519, 55690144728, 53090086057

Offset: 0

Author

Peter Luschny, May 30 2017

Keywords

• nonn
• tabl

Examples

			Triangle starts:
0: [1]
1: [0, 1]
2: [0, 1,      7]
3: [0, 1,     52,      163]
4: [0, 1,    341,     4499,       8983]
5: [0, 1,   2246,    98256,     660746,      966751]
6: [0, 1,  15177,  2045282,   35677082,   155729277,   179781181]
7: [0, 1, 104952, 42658239, 1754605504, 17446464519, 55690144728, 53090086057]
...
Let q4(x) = (x + 341*x^2 + 4499*x^3 + 8983*x^4) / (1-x)^5 then the coefficients of the series expansion of q4 are column 4 of A287698.
		

Crossrefs

Cf. A000442, A212856, A287696, A287698.

Programs

Maple

A287697_row := n -> Delta(A287696_poly(n), n): # Delta defined in A287315.
for n from 0 to 9 do A287697_row(n) od;
A287697_eulerian := (n,x) -> add(A287697_row(n)[k+1]*x^k,k=0..n)/(1-x)^(n+1):
for n from 0 to 4 do A287697_eulerian(n,x) od;

Formula

T(n,n) = A212856(n).

Sum_{k=0..n} T(n,k) = A000442(n).