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A027478 Triangle of the cube of the normalized, unsigned Stirling matrix of the first kind. 7
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The absolute values are unchanged if one uses the signed Stirling numbers of the first kind.

LINKS

Table of n, a(n) for n=1..36.

FORMULA

Let A be the lower triangular matrix with entries a[ i, j ] = (-1)^(i+j)*s(i, j)/i! if j<=i, 0 if j>i, where s(i,j) is the Stirling number of the first kind. Let N be the column vector ((i!^3)).

T is the lower triangular matrix  A.A.A.N.

EXAMPLE

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,

...

MATHEMATICA

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]]

CROSSREFS

Cf. A027477 for the quadratic version.

Cf. A027479 for the quartic version.

Cf. A027482 is the first subdiagonal of this triangle.

Sequence in context: A138324 A052122 A027538 * A009792 A103243 A027496

Adjacent sequences:  A027475 A027476 A027477 * A027479 A027480 A027481

KEYWORD

nonn,tabl,easy

AUTHOR

Olivier Gérard

EXTENSIONS

Definition, formula and program edited for clarity by Olivier Gérard, Jan 20 2019

STATUS

approved

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)