A343804 - OEIS

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A343804

T(n, k) = Sum_{j=k..n} binomial(n, j)*E2(j, j-k), where E2 are the Eulerian numbers A201637. Triangle read by rows, T(n, k) for 0 <= k <= n.

1, 1, 1, 1, 4, 1, 1, 15, 11, 1, 1, 64, 96, 26, 1, 1, 325, 824, 448, 57, 1, 1, 1956, 7417, 6718, 1779, 120, 1, 1, 13699, 71595, 96633, 43411, 6429, 247, 1, 1, 109600, 746232, 1393588, 944618, 243928, 21898, 502, 1, 1, 986409, 8403000, 20600856, 19521210, 7739362, 1250774, 71742, 1013, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

Triangle starts:

[0] 1

[1] 1, 1

[2] 1, 4, 1

[3] 1, 15, 11, 1

[4] 1, 64, 96, 26, 1

[5] 1, 325, 824, 448, 57, 1

[6] 1, 1956, 7417, 6718, 1779, 120, 1

[7] 1, 13699, 71595, 96633, 43411, 6429, 247, 1

[8] 1, 109600, 746232, 1393588, 944618, 243928, 21898, 502, 1

[9] 1, 986409, 8403000, 20600856, 19521210, 7739362, 1250774, 71742, 1013, 1

MAPLE

T := (n, k) -> add(binomial(n, r)*combinat:-eulerian2(r, r-k), r = k..n):

seq(seq(T(n, k), k = 0..n), n = 0..9);

CROSSREFS

Row sums: A084262.

Cf. A046802 (Eulerian first order).

Sequence in context: A208956 A271705 A320280 * A157211 A176428 A116469

Adjacent sequences: A343801 A343802 A343803 * A343805 A343806 A343807

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Apr 30 2021

STATUS

approved