A178802 Irregular triangle T(n,k) = A048996(n,k) * A178801(n,k), read by rows, 1 <= k <= A000041(n).

1, 1, 2, 2, 6, 12, 6, 24, 48, 24, 72, 24, 120, 240, 240, 360, 360, 480, 120, 720, 1440, 1440, 720, 2160, 4320, 720, 2880, 4320, 3600, 720, 5040, 10080, 10080, 10080, 15120, 30240, 15120, 15120, 20160, 60480, 20160, 25200, 50400, 30240, 5040, 40320, 80640, 80640, 80640, 40320, 120960

Offset

0,3

Comments

Rows have A000041(n) entries, with partitions in Abramowitz and Stegun order (A036036).

Links

Andrew Howroyd, Table of n, a(n) for n = 0..2713 (rows 0..20)

Formula

T(n,k) = A048996(n,k) * A178801(n,k) = A048996(n,k) * n!.

Example

Triangle begins:
   0 |   1;
   1 |   1;
   2 |   2,    2;
   3 |   6,   12,    6;
   4 |  24,   48,   24,  72,   24;
   5 | 120,  240,  240, 360,  360,  480, 120;
   6 | 720, 1440, 1440, 720, 2160, 4320, 720, 2880, 4320, 3600, 720;
    ...

Prog

(PARI)
C(sig)={my(S=Set(sig)); (#sig)!/prod(k=1, #S, (#select(t->t==S[k], sig))!)}
Row(n)={n!*apply(C, [Vecrev(p) | p<-partitions(n)])}
{ for(n=0, 7, print(Row(n))) } \\ Andrew Howroyd, Oct 02 2025

Crossrefs

Cf. A000041 (row lengths), A002866 (row sums), A036036, A048996, A178801.

Sequence in context: A351081 A241669 A356546 * A156992 A285529 A305215

Adjacent sequences: A178799 A178800 A178801 * A178803 A178804 A178805

Keyword

easy,nonn,tabf

Author

Alford Arnold, Jun 15 2010

Extensions

Name improved by Andrew Howroyd, Oct 02 2025

Status

approved