A356013 Triangle T(n,k), n >= 1, 1 <= k <= n, read by rows, where T(n,k) = n!/(k! * floor(n/k)).

1, 1, 1, 2, 3, 1, 6, 6, 4, 1, 24, 30, 20, 5, 1, 120, 120, 60, 30, 6, 1, 720, 840, 420, 210, 42, 7, 1, 5040, 5040, 3360, 840, 336, 56, 8, 1, 40320, 45360, 20160, 7560, 3024, 504, 72, 9, 1, 362880, 362880, 201600, 75600, 15120, 5040, 720, 90, 10, 1

Offset

1,4

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

Triangle begins:
      1;
      1,     1;
      2,     3,     1;
      6,     6,     4,    1;
     24,    30,    20,    5,    1;
    120,   120,    60,   30,    6,   1;
    720,   840,   420,  210,   42,   7,  1;
   5040,  5040,  3360,  840,  336,  56,  8, 1;
  40320, 45360, 20160, 7560, 3024, 504, 72, 9, 1;
  ...

Prog

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

Crossrefs

Row sums gives A356011.

Column k=1..3 give A000142(n-1), |A265376(n)|, A356012.

Cf. A355996.

Sequence in context: A035485 A074306 A294218 * A366139 A347945 A036039

Adjacent sequences: A356010 A356011 A356012 * A356014 A356015 A356016

Keyword

nonn,tabl

Author

Seiichi Manyama, Jul 23 2022

Status

approved