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A271697 Triangle read by rows, T(n,k) = Sum_{j=0..n} C(-j-1,-n-1)*E1(j,k), E1 the Eulerian numbers A173018, for n>=0 and 0<=k<=n. 3
1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 7, 1, 0, 0, 1, 21, 21, 1, 0, 0, 1, 51, 161, 51, 1, 0, 0, 1, 113, 813, 813, 113, 1, 0, 0, 1, 239, 3361, 7631, 3361, 239, 1, 0, 0, 1, 493, 12421, 53833, 53833, 12421, 493, 1, 0, 0, 1, 1003, 42865, 320107, 607009, 320107, 42865, 1003, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Table of n, a(n) for n=0..65.

Peter Luschny, Extensions of the binomial

EXAMPLE

Triangle starts:

1,

0, 0,

0, 1, 0,

0, 1, 1, 0,

0, 1, 7, 1, 0,

0, 1, 21, 21, 1, 0,

0, 1, 51, 161, 51, 1, 0,

0, 1, 113, 813, 813, 113, 1, 0.

MAPLE

A271697 := (n, k) -> add(binomial(-j-1, -n-1)*combinat:-eulerian1(j, k), j=0..n):

seq(seq(A271697(n, k), k=0..n), n=0..11);

MATHEMATICA

<<Combinatorica`

Flatten[Table[Sum[Binomial[-j-1, -n-1] Eulerian[j, k], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]

CROSSREFS

Variant: A046739 (main entry for this triangle).

A000166 (row sums), A122045 (Euler numbers are the alternating row sums), A070313 (col. 2) and (diag. n,n-2).

Cf. A173018.

Sequence in context: A036949 A059515 A136428 * A226371 A298937 A223855

Adjacent sequences:  A271694 A271695 A271696 * A271698 A271699 A271700

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Apr 12 2016

STATUS

approved

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Last modified February 24 08:59 EST 2020. Contains 332209 sequences. (Running on oeis4.)