A358366 - OEIS

A358366

Table read by rows. T(n, k) = [x^k] n! * Sum_{j=0..n} binomial(n*x, j).

1, 1, 1, 2, 2, 4, 6, 15, 0, 27, 24, 56, 176, -128, 256, 120, 470, 125, 3125, -3125, 3125, 720, 2664, 10944, -16200, 71280, -69984, 46656, 5040, 26796, 17836, 376957, -840350, 1882384, -1647086, 823543, 40320, 204672, 1022720, -2222080, 16257024, -34865152, 55050240, -41943040, 16777216

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

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..44.

EXAMPLE

[n\k] 0 1 2 3 4 5 6 7 [Sum]

--------------------------------------------------------------------------

[0] 1; [1]

[1] 1, 1; [2]

[2] 2, 2, 4; [8]

[3] 6, 15, 0, 27; [48]

[4] 24, 56, 176, -128, 256; [384]

[5] 120, 470, 125, 3125, -3125, 3125; [3840]

[6] 720, 2664, 10944, -16200, 71280, -69984, 46656; [46080]

[7] 5040, 26796, 17836, 376957, -840350, 1882384, -1647086, 823543; [645120]

MAPLE

Trow := proc(n) expand(n!*add(binomial(n*x, j), j = 0..n));

seq(coeff(%, x, k), k=0..n) end: seq(print(Trow(n)), n = 0..8);

CROSSREFS

Cf. T(n, 0) = n! (A000142), T(n, n) = n^n (A000312), A000165 (row sums).

Sequence in context: A116637 A153961 A134041 * A069925 A357951 A227315

Adjacent sequences: A358363 A358364 A358365 * A358367 A358368 A358369

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Nov 12 2022

STATUS

approved