A027486
First column of triangle A027477, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
1, 3, 23, 330, 7604, 256620, 11923260, 729524880, 56840099904, 5493503695680, 644870893060800, 90366972897801600, 14899694352066120960, 2855250418022402400000, 629258349435218754451200, 158034681938560927788288000, 44866854739192779425625292800
Offset: 1
Cf.
A027477 (Square of normalized Stirling matrix of the first kind).
A027481
Second subdiagonal of triangle A027477, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
23, 215, 1035, 3535, 9730, 23058, 48930, 95370, 173745, 299585, 493493, 782145, 1199380, 1787380, 2597940, 3693828, 5150235, 7056315, 9516815, 12653795, 16608438, 21542950, 27642550, 35117550, 44205525, 55173573, 68320665, 83980085, 102521960, 124355880
Offset: 3
A027487
Second column of triangle A027477, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
1, 12, 215, 5700, 212464, 10645152, 691560092, 56600396640, 5701663652256, 693513787887360, 100238236943757120, 16984716659427928320, 3334997046159250716672, 751255152802084700098560, 192454224298697834146195200, 55636762557552859712661811200
Offset: 2
Cf.
A027477 (Square of normalized Stirling matrix of the first kind).
A027488
Third column of triangle A027477, constructed from the Stirling numbers of the first kind.
Original entry on oeis.org
1, 30, 1035, 45675, 2582209, 183962268, 16206744140, 1734708878100, 222083697846516, 33544055541553128, 5906505211210055088, 1199823052824417425040, 278598452852079082857744, 73346715446248518553100160, 21736011315987768499695624960
Offset: 3
Cf.
A027477 (Square of normalized Stirling matrix 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
A027479
Triangle of the fourth power of the normalized, unsigned Stirling matrix of the first kind.
Original entry on oeis.org
1, 15, 1, 1175, 120, 1, 294330, 36935, 510, 1, 181082204, 25816200, 460035, 1560, 1, 231844265940, 36133755364, 757122975, 3411835, 3885, 1, 551220029003580, 91850446178400, 2159098539409, 11690792400, 18037810, 8400, 1, 2239429013789400720, 393327895035809180, 10088942720014620, 62324463343569, 117282133080, 75042450, 16380, 1
Offset: 1
First rows of the triangle are:
1;
15, 1;
1175, 120, 1;
294330, 36935, 510, 1;
181082204, 25816200, 460035, 1560, 1;
...
-
Module[{nmax=8,m},m=(Table[Table[(-1)^(i+j) StirlingS1[i,j]/i!,{j,1,nmax}],{i,1,nmax}]);m=m.m.m.m*Table[i!^4,{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
Showing 1-6 of 6 results.
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