A370418 - OEIS

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A370418

Triangle read by rows. T(n, k) = (n - k)! * (n + k)!.

0

1, 1, 2, 4, 6, 24, 36, 48, 120, 720, 576, 720, 1440, 5040, 40320, 14400, 17280, 30240, 80640, 362880, 3628800, 518400, 604800, 967680, 2177280, 7257600, 39916800, 479001600, 25401600, 29030400, 43545600, 87091200, 239500800, 958003200, 6227020800, 87178291200

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

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..35.

FORMULA

Sum_{k=0..n} (-1)^k*T(n, k) = n!^2 / 2 + (-1)^n * (2*n + 2)! / (2*n + 2)^2.

EXAMPLE

Triangle starts:

[0] 1;

[1] 1, 2;

[2] 4, 6, 24;

[3] 36, 48, 120, 720;

[4] 576, 720, 1440, 5040, 40320;

[5] 14400, 17280, 30240, 80640, 362880, 3628800;

[6] 518400, 604800, 967680, 2177280, 7257600, 39916800, 479001600;

MAPLE

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

seq(seq(T(n, k), k = 0..n), n = 0..7);

MATHEMATICA

Table[(n - k)!*(n + k)!, {n, 0, 7}, {k, 0, n}] // Flatten (* Michael De Vlieger, Mar 05 2024 *)

CROSSREFS

Cf. A010050 (main diagonal), A009445 (subdiagonal), A001044 (column 0), A175430 (column 1), A024420 (bisection is alternating sum).

Cf. A119502, A143084.

Sequence in context: A086172 A261832 A141526 * A226169 A343728 A261746

Adjacent sequences: A370415 A370416 A370417 * A370419 A370420 A370421

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Feb 27 2024

STATUS

approved