cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A144891 Lower triangular array called S1hat(5) related to partition number array A144890.

Original entry on oeis.org

1, 5, 1, 30, 5, 1, 210, 55, 5, 1, 1680, 360, 55, 5, 1, 15120, 3630, 485, 55, 5, 1, 151200, 29820, 4380, 485, 55, 5, 1, 1663200, 321300, 39570, 5005, 485, 55, 5, 1, 19958400, 3225600, 421800, 43320, 5005, 485, 55, 5, 1, 259459200, 38808000, 4265100, 470550, 46445, 5005
Offset: 1

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Author

Wolfdieter Lang Oct 09 2008

Keywords

Comments

If in the partition array M31hat(5):=A144890 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(5). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.
The first columns are A001720(n+3)=(n+3)!/4!, A144893, A144894,...

Examples

			[1];[5,1];[30,5,1];[210,55,5,1];[1680,360,55,5,1];...
		

Crossrefs

A144892 (row sums).

Formula

a(n,m)=sum(product(|S1(5;j,1)|^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S1(5,n,1)|= A049353(n,1) = A001720(n+3) = (n+3)!/4!.

A144894 Third column (m=3) of triangle A144891 (S1hat(5)).

Original entry on oeis.org

1, 5, 55, 485, 4380, 39570, 421800, 4265100, 49455000, 594001800, 7784683200, 107814672000, 1624964544000, 25881953328000, 443107288512000, 8028628336512000, 154539996629760000, 3135393617489280000, 67045955961922560000, 1503619681171829760000, 35321502985569884160000
Offset: 0

Views

Author

Wolfdieter Lang, Oct 09 2008

Keywords

Crossrefs

Cf. A144891, A001720 (first column), A144893 (second column).

Formula

a(n) = A144891(n+3,3), n>=0.
Showing 1-2 of 2 results.