A355996 - OEIS

A355996

Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)!).

1, 1, 1, 1, 3, 1, 1, 6, 4, 1, 1, 30, 20, 5, 1, 1, 60, 60, 30, 6, 1, 1, 420, 420, 210, 42, 7, 1, 1, 840, 3360, 840, 336, 56, 8, 1, 1, 7560, 10080, 7560, 3024, 504, 72, 9, 1, 1, 15120, 100800, 75600, 15120, 5040, 720, 90, 10, 1, 1, 166320, 1108800, 831600, 166320, 55440, 7920, 990, 110, 11, 1

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..66.

FORMULA

E.g.f. of column k: (1 - x^k) * (exp(x^k) - 1)/(k! * (1 - x)).

EXAMPLE

Triangle begins:

1, 1;

1, 3, 1;

1, 6, 4, 1;

1, 30, 20, 5, 1;

1, 60, 60, 30, 6, 1;

1, 420, 420, 210, 42, 7, 1;

1, 840, 3360, 840, 336, 56, 8, 1;

...

MATHEMATICA

T[n_, k_] := n!/(k!*Floor[n/k]!); Table[T[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 22 2022 *)

PROG

(PARI) T(n, k) = n!/(k!*(n\k)!);

CROSSREFS

Row sums give A355991.

Column k=1..3 give A000012, A355989, A355990.

Sequence in context: A208334 A162430 A305059 * A128101 A211351 A124802

Adjacent sequences: A355993 A355994 A355995 * A355997 A355998 A355999

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jul 22 2022

STATUS

approved