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A156594 A q-Stirling 2nd triangle sequence:q=3;m=2; t(n,k)=If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ 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])]. 0
1, 1, 1, 1, -3, 1, 1, 6, 6, 1, 1, -3, 6, -3, 1, 1, -21, -21, -21, -21, 1, 1, 24, 168, -84, 168, 24, 1, 1, 195, -1560, 5460, 5460, -1560, 195, 1, 1, -111, 7215, 28860, 202020, 28860, 7215, -111, 1, 1, -3072, -113664, -3694080, 29552640, 29552640, -3694080 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -1, 14, 2, -82, 302, 8192, 273950, 51483650, -4132493224,...}.

On the sequence only q=2 and q=3 are Integers,

the rest have a few rational terms.

LINKS

Table of n, a(n) for n=0..51.

FORMULA

q=3;m=2;

t(n,k)=If[m == 0, n!, Product[Sum[(-1)^i*StirlingS2[ 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])].

EXAMPLE

{1},

{1, 1},

{1, -3, 1},

{1, 6, 6, 1},

{1, -3, 6, -3, 1},

{1, -21, -21, -21, -21, 1},

{1, 24, 168, -84, 168, 24, 1},

{1, 195, -1560, 5460, 5460, -1560, 195, 1},

{1, -111, 7215, 28860, 202020, 28860, 7215, -111, 1},

{1, -3072, -113664, -3694080, 29552640, 29552640, -3694080, -113664, -3072, 1},

{1, -4053, -4150272, 76780032, -4990702080, 5703659520, -4990702080, 76780032, -4150272, -4053, 1}

MATHEMATICA

t[n_, m_] = If[m == 0, n!, Product[Sum[(-1)^i* StirlingS2[k - 1, i]*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];

b[n_, k_, m_] = f[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

Sequence in context: A159572 A190907 A035582 * A109647 A176668 A054120

Adjacent sequences:  A156591 A156592 A156593 * A156595 A156596 A156597

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 10 2009

STATUS

approved

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)