A344565 - OEIS

A344565

Triangle read by rows, for 0 <= k <= n: T(n, k) = binomial(n, k) * binomial(binomial(n + 3, 2), 2).

3, 15, 15, 45, 90, 45, 105, 315, 315, 105, 210, 840, 1260, 840, 210, 378, 1890, 3780, 3780, 1890, 378, 630, 3780, 9450, 12600, 9450, 3780, 630, 990, 6930, 20790, 34650, 34650, 20790, 6930, 990, 1485, 11880, 41580, 83160, 103950, 83160, 41580, 11880, 1485

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

OFFSET

0,1

LINKS

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

FORMULA

T(n, k) = (n + 4)! / (8 * k! * (n - k)!).

EXAMPLE

Triangle begins:

[0] 3;

[1] 15, 15;

[2] 45, 90, 45;

[3] 105, 315, 315, 105;

[4] 210, 840, 1260, 840, 210;

[5] 378, 1890, 3780, 3780, 1890, 378;

[6] 630, 3780, 9450, 12600, 9450, 3780, 630;

[7] 990, 6930, 20790, 34650, 34650, 20790, 6930, 990;

[8] 1485, 11880, 41580, 83160, 103950, 83160, 41580, 11880, 1485;

[9] 2145, 19305, 77220, 180180, 270270, 270270, 180180, 77220, 19305, 2145.

MAPLE

T := (n, k) -> (n + 4)! / (8 * k! * (n - k)!):

for n from 0 to 9 do seq(T(n, k), k = 0..n) od;

MATHEMATICA

T[n_, k_] := (n + 4)!/(8*k!*(n - k)!); Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, May 28 2021 *)

CROSSREFS

Apparently a subtriangle of A344678. Row sums A344564.

Sequence in context: A279534 A181404 A096672 * A289374 A289103 A289403

Adjacent sequences: A344562 A344563 A344564 * A344566 A344567 A344568

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, May 28 2021

STATUS

approved

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