A027485
Second subdiagonal of triangle A027479, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
1175, 36935, 460035, 3411835, 18037810, 75042450, 261050370, 790412370, 2142018945, 5301812945, 12168481325, 26200706805, 53409827380, 103832238580, 193651833780, 348184665300, 605986277115, 1024397262315, 1686904988615, 2712769566815, 4269440463750
Offset: 3
Cf.
A027479 (fourth power of the triangular matrix of the Stirling numbers of the first kind).
A027492
First column of Triangle A027479, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
1, 15, 1175, 294330, 181082204, 231844265940, 551220029003580, 2239429013789400720, 14591040654287257562304, 145033009542380637757759680, 2112192468307817772279540177600
Offset: 1
Cf.
A027479 (fourth power of the triangular matrix of the Stirling numbers of the first kind).
A027493
Second column of Triangle A027479, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
1, 120, 36935, 25816200, 36133755364, 91850446178400, 393327895035809180, 2675039498159452367040, 27560317167934730312259456, 413843767423449662598795745920, 8770587574512577781320579427273280
Offset: 2
Cf.
A027479 (fourth power of the triangular matrix of the Stirling numbers of the first kind).
A027494
Third column of Triangle A027479, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
1, 510, 460035, 757122975, 2159098539409, 10088942720014620, 73537595144196109100, 801932992091138324924100, 12630702915931923419085563316, 278859508455542166912631908053160
Offset: 3
Cf.
A027479 (fourth power of the triangular matrix of the Stirling numbers of the first kind).
A027478
Triangle of the cube of the normalized, unsigned Stirling matrix of the first kind.
Original entry on oeis.org
1, 7, 1, 176, 39, 1, 10746, 2951, 126, 1, 1297704, 407450, 22535, 310, 1, 272866980, 94128364, 6139575, 112435, 645, 1, 91570835040, 33910601508, 2487385684, 54814095, 426475, 1197, 1, 46034917019280, 18030534782364, 1446119232796, 36402686929, 345710680, 1333906, 2044, 1
Offset: 1
The first rows of the triangle are :
1,
7, 1,
176, 39, 1,
10746, 2951, 126, 1,
1297704, 407450, 22535, 310, 1,
272866980, 94128364, 6139575, 112435, 645, 1,
...
Cf.
A027477 for the quadratic version.
Cf.
A027479 for the quartic version.
Cf.
A027482 is the first subdiagonal of this triangle.
-
Module[{nmax=8,m},m=(Table[Table[(-1)^(i+j) StirlingS1[i,j]/i!,{j,1,nmax}],{i,1,nmax}]);m=m.m.m*Table[i!^3,{i,1,nmax}]; Flatten[Table[Table[m[[i,j]],{j,1,i}],{i,1,nmax}],1]]
Definition, formula and program edited for clarity by
Olivier Gérard, Jan 20 2019
A027477
Triangle of the square of the normalized, unsigned Stirling matrix of the first kind.
Original entry on oeis.org
1, 3, 1, 23, 12, 1, 330, 215, 30, 1, 7604, 5700, 1035, 60, 1, 256620, 212464, 45675, 3535, 105, 1, 11923260, 10645152, 2582209, 241080, 9730, 168, 1, 729524880, 691560092, 183962268, 19661649, 970200, 23058, 252, 1
Offset: 1
First rows of the triangle are:
1,
3,1,
23,12,1,
330,215,30,1,
7604,5700,1035,60,1,
256620,212464,45675,3535,105,1
...
-
Module[{nmax=8,m},m=(Table[Table[(-1)^(i+j) StirlingS1[i,j]/i!,{j,1,nmax}],{i,1,nmax}]);m=m.m*Table[i!^2,{i,1,nmax}]; Flatten[Table[Table[m[[i,j]],{j,1,i}],{i,1,nmax}],1]]
Definition, formula and program edited for clarity by
Olivier Gérard, Jan 20 2019
A027484
a(n) = n*(n^4-1)/2.
Original entry on oeis.org
15, 120, 510, 1560, 3885, 8400, 16380, 29520, 49995, 80520, 124410, 185640, 268905, 379680, 524280, 709920, 944775, 1238040, 1599990, 2042040, 2576805, 3218160, 3981300, 4882800, 5940675, 7174440, 8605170, 10255560, 12149985
Offset: 2
- Vincenzo Librandi, Table of n, a(n) for n = 2..1000
- S. Gartenhaus, Odd Order Pandiagonal Latin and Magic Cubes in Three and Four Dimensions, arXiv:math/0210275 [math.CO], 2002.
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
-
[n*(n^4 - 1)/2: n in [2..50]];// Vincenzo Librandi, Dec 29 2012
-
Table[(m^5 - m)/2, {m, 34}] (* Zerinvary Lajos, Mar 21 2007 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{15,120,510,1560,3885,8400},30] (* Harvey P. Dale, Aug 02 2024 *)
-
a(n)=n*(n^4-1)/2 \\ Charles R Greathouse IV, Oct 21 2022
Showing 1-7 of 7 results.
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