The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A343804 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#10 by Bruno Berselli at Fri Apr 30 10:56:02 EDT 2021

STATUS

reviewed

approved

#9 by Joerg Arndt at Fri Apr 30 09:54:29 EDT 2021

STATUS

proposed

reviewed

#8 by Peter Luschny at Fri Apr 30 09:14:18 EDT 2021

STATUS

editing

proposed

#7 by Peter Luschny at Fri Apr 30 09:14:12 EDT 2021

NAME

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.

STATUS

proposed

editing

#6 by Peter Luschny at Fri Apr 30 09:13:47 EDT 2021

STATUS

editing

proposed

#5 by Peter Luschny at Fri Apr 30 09:07:00 EDT 2021

EXAMPLE

[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

#4 by Peter Luschny at Fri Apr 30 09:05:14 EDT 2021

CROSSREFS

Row sums: A084262.

#3 by Peter Luschny at Fri Apr 30 09:02:03 EDT 2021

NAME

allocated (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 Peter Luschny0 <= k <= n.

DATA

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

OFFSET

0,5

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

Cf. A046802 (Eulerian first order).

KEYWORD

allocated

nonn,tabl

AUTHOR

Peter Luschny, Apr 30 2021

STATUS

approved

editing

#2 by Peter Luschny at Fri Apr 30 08:52:20 EDT 2021

KEYWORD

allocating

allocated

#1 by Peter Luschny at Fri Apr 30 08:52:20 EDT 2021

NAME

allocated for Peter Luschny

KEYWORD

allocating

STATUS

approved