A179863 Irregular triangle T(n,k) = A049085(n,k)!, read by rows, 1 <= k <= A000041(n).

1, 1, 2, 1, 6, 2, 1, 24, 6, 2, 2, 1, 120, 24, 6, 6, 2, 2, 1, 720, 120, 24, 6, 24, 6, 2, 6, 2, 2, 1, 5040, 720, 120, 24, 120, 24, 6, 6, 24, 6, 2, 6, 2, 2, 1, 40320, 5040, 720, 120, 24, 720, 120, 24, 24, 6, 120, 24, 6, 6, 2, 24, 6, 2, 6, 2, 2, 1, 362880, 40320, 5040, 720, 120, 5040, 720, 120

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) = A000142(A049085(n,k)).

Example

A049085 begins
  0
  1
  2 1
  3 2 1
  4 3 2 2 1
  5 4 3 3 2 2 1
  ...
so this triangle begins
  1
  1
  2 1
  6 2 1
  24 6 2 2 1
  120 24 6 6 2 2 1
  ...

Prog

(PARI) Row(n)=if(n==0, [1], [vecmax(Vec(p))! | p<-partitions(n)])
{ for(n=0, 7, print(Row(n))) } \\ Andrew Howroyd, Oct 02 2025

Crossrefs

Cf. A000041 (row lengths), A000142, A036036, A101880 (row sums).

Sequence in context: A106187 A110135 A335109 * A069123 A134133 A157392

Adjacent sequences: A179860 A179861 A179862 * A179864 A179865 A179866

Keyword

easy,nonn,tabf

Author

Alford Arnold, Jul 29 2010

Extensions

a(0)=1 prepended by Andrew Howroyd, Oct 02 2025

Status

approved