A287697 - OEIS

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

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..35.

FORMULA

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

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

EXAMPLE

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.

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;

CROSSREFS

Cf. A000442, A212856, A287696, A287698.

Sequence in context: A222063 A395236 A156960 * A335953 A227958 A118858

Adjacent sequences: A287694 A287695 A287696 * A287698 A287699 A287700

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, May 30 2017

STATUS

approved