A178803 Write the factorial of each term in A036043(n).

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

Offset

1,3

Comments

Sequence A036043 measures the length of numeric partitions.

Links

Table of n, a(n) for n=1..83.

Example

A036043 begins 1 1 2 1 2 3 1 2 2 3 4 1 2 2 3 3 4 5 ...
so this table begins 1 1 2 1 2 6 1 2 2 6 24 ...
1;
1, 2;
1, 2, 6;
1, 2, 2, 6, 24;
1, 2, 2, 6, 6, 24, 120;
1, 2, 2, 2, 6, 6, 6, 24, 24, 120, 720;
1, 2, 2, 2, 6, 6, 6, 6, 24, 24, 24, 120, 120, 720, 5040;
1, 2, 2, 2, 2, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 120, 120, 120, 720, 720, 5040, 40320;

Prog

(SageMath)
def A178803_row(n):
    return [factorial(len(p)) for k in (0..n) for p in Partitions(n, length=k)]
for n in (0..10): print(A178803_row(n)) # Peter Luschny, Nov 02 2019

Crossrefs

Cf. A000041 (shape sequence), A000142 (factorials), A036043, A101880 (row sums).

Sequence in context: A144358 A049404 A159885 * A292901 A083773 A129116

Adjacent sequences: A178800 A178801 A178802 * A178804 A178805 A178806

Keyword

easy,nonn,tabf

Author

Alford Arnold, Jun 17 2010

Status

approved