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.

Showing 1-4 of 4 results.

A144892 Row sums of triangle A144891 (S1hat(5)).

Original entry on oeis.org

1, 6, 36, 271, 2101, 19296, 185946, 2029621, 23654671, 303054846, 4153493496, 61501843771, 969988075021, 16326593796396, 291081828746646, 5490558646391521, 109092080140450771, 2278805715594223146, 49897959213869259396, 1143087784199443461271
Offset: 0

Views

Author

Wolfdieter Lang, Oct 09 2008

Keywords

Crossrefs

Cf. A144891.

Formula

a(n) = Sum_{m=1..n} A144891(n,m), n>=1.

A144893 Second column (m=2) of triangle A144891 (S1hat(5)).

Original entry on oeis.org

1, 5, 55, 360, 3630, 29820, 321300, 3225600, 38808000, 466300800, 6360379200, 89703936000, 1389213504000, 22565765376000, 394272204480000, 7248941973504000, 141496402037760000, 2901258659819520000, 62617333274496000000, 1414755114367795200000, 33446554797269053440000
Offset: 0

Views

Author

Wolfdieter Lang, Oct 09 2008

Keywords

Crossrefs

Cf. A144891, A001720 (first column), A144894 (third column).

Formula

a(n) = A144891(n+2,2), n>=0.

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.

A144890 Partition number array, called M31hat(5).

Original entry on oeis.org

1, 5, 1, 30, 5, 1, 210, 30, 25, 5, 1, 1680, 210, 150, 30, 25, 5, 1, 15120, 1680, 1050, 900, 210, 150, 125, 30, 25, 5, 1, 151200, 15120, 8400, 6300, 1680, 1050, 900, 750, 210, 150, 125, 30, 25, 5, 1, 1663200, 151200, 75600, 50400, 44100, 15120, 8400, 6300, 5250, 4500
Offset: 1

Views

Author

Wolfdieter Lang Oct 09 2008, Oct 28 2008

Keywords

Comments

Each partition of n, ordered as in Abramowitz-Stegun (A-St order; for the reference see A134278), is mapped to a nonnegative integer a(n,k) =: M31hat(5;n,k) with the k-th partition of n in A-St order.
The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].
Fourth member (K=5) in the family M31hat(K) of partition number arrays.
If M31hat(5;n,k) is summed over those k with fixed number of parts m one obtains the unsigned triangle S1hat(5):= A144891.

Examples

			[1];[5,1];[30,5,1];[210,30,25,5,1];[1680,210,150,30,25,5,1];...
a(4,3)= 25 = |S1(5;2,1)|^2. The relevant partition of 4 is (2^2).

Links

Crossrefs

Cf. A144892 (row sums).
Cf. A144885 (M31hat(4) array). A144891 (S1hat(5)).

Formula

a(n,k) = product(|S1(5;j,1)|^e(n,k,j),j=1..n) with |S1(5;n,1)| = A049353(n,1) = A001720(n+3) = [1,5,30,210,1680,...] = (n+3)!/4!, n>=1 and the exponent e(n,k,j) of j in the k-th partition of n in the A-St ordering of the partitions of n.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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