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A156584 Triangle read by rows, T(n,k) = SF(n-1)/(SF(n-k)*SF(k)) where SF(n) is the superfactorial A000178(n); n>=0, 1<=k<=n-1. 1
1, 1, 1, 1, 3, 1, 1, 12, 12, 1, 1, 60, 240, 60, 1, 1, 360, 7200, 7200, 360, 1, 1, 2520, 302400, 1512000, 302400, 2520, 1, 1, 20160, 16934400, 508032000, 508032000, 16934400, 20160, 1, 1, 181440, 1219276800, 256048128000, 1536288768000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are: 1, 2, 5, 26, 362, 15122, 2121842, 1049973122, 2050823940482, 15854719559212802, 552278629803518956802, ... .

LINKS

Table of n, a(n) for n=0..40.

EXAMPLE

{1},

{1, 1},

{1, 3, 1},

{1, 12, 12, 1},

{1, 60, 240, 60, 1},

{1, 360, 7200, 7200, 360, 1},

{1, 2520, 302400, 1512000, 302400, 2520, 1},

{1, 20160, 16934400, 508032000, 508032000, 16934400, 20160, 1},

{1, 181440, 1219276800, 256048128000, 1536288768000, 256048128000, 1219276800, 181440, 1}

MAPLE

SF := n -> mul(j!, j=0..n): T := (n, k) -> SF(n-1)/(SF(n-k)*SF(k)):

seq(print(seq(T(n, k), k=1..n-1)), n=0..9); # Peter Luschny, Jan 24 2015

MATHEMATICA

t[n_, m_] = If[m == 0, n!, Product[Sum[(-1)^(i + k)*StirlingS1[k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];

Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]

CROSSREFS

Cf. A009963.

Sequence in context: A098778 A078122 A128592 * A209424 A129619 A094573

Adjacent sequences:  A156581 A156582 A156583 * A156585 A156586 A156587

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 10 2009

EXTENSIONS

New name and editing, Peter Luschny, Jan 24 2015

STATUS

approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)