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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A089516 Denominators used in A089515 to compute the column sequences of triangle A090215.

Original entry on oeis.org

1, 4, 56, 5712, 18786768, 955776822000, 744550144338000, 187882017072683934000, 114232266380191831872000, 1559289924571192031300084690688000
Offset: 1

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Author

Wolfdieter Lang, Dec 01 2003

Keywords

Formula

a(n) = lcm(seq(denominator(a(n, m)), m=1..n)) with the a(n, m) formula given in A089515(n, m) but without the D(n) factor in front and lcm denotes the least common multiple of a set of numbers.

A090215 A generalization of triangles A071951 (Legendre-Stirling) and A089504.

Original entry on oeis.org

1, 24, 1, 576, 144, 1, 13824, 17856, 504, 1, 331776, 2156544, 199296, 1344, 1, 7962624, 259117056, 73903104, 1328256, 3024, 1, 191102976, 31102009344, 26864234496, 1189638144, 6408576, 6048, 1, 4586471424, 3732432224256, 9702226427904, 1026160275456, 11956045824, 24697728, 11088, 1
Offset: 1

Views

Author

Wolfdieter Lang, Dec 01 2003

Keywords

Comments

This triangle underlies the array entry A090214 ((4,4)-generalized Stirling2).

Examples

			[1]; [24,1]; [576,144,1]; [13824,17856,504,1]; ...
		

Crossrefs

Cf. A071951 (Legendre-Stirling, (2, 2) case), A089504 ((3, 3)-case).
The column sequences (without leading zeros) are A009968 (powers of 24), etc.

Programs

  • Mathematica
    max = 10; f[m_] := 1/Product[1-FactorialPower[r+3, 4]*x, {r, 1, m}]; col[m_] := CoefficientList[f[m] + O[x]^(max-m+1), x]; a[n_, m_] := col[m][[n-m+1]]; Table[a[n, m], {n, 1, max}, {m, 1, n}] // Flatten (* Jean-François Alcover, Sep 01 2016 *)

Formula

G.f. for m-th column sequence (without leading zeros and m>=1) is 1/product(1-fallfac(r+3, 4)*x, r=1..m) with fallfac(n, k) := A008279(n, k) (falling factorials).
a(n, m) = sum(A089515(m, p)*fallfac(p, 4)^(n-m), p=1..m)/D(m) if n>=m>=1 else 0; with D(m) := A089516(m).

Extensions

More terms coming from a-file added by Michel Marcus, Feb 08 2023
Showing 1-2 of 2 results.