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A156593 A q-Stirling 2nd triangle sequence:q=2;m=1; 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, -2, 1, 1, 2, 2, 1, 1, 2, -2, 2, 1, 1, -6, 6, 6, -6, 1, 1, -14, -42, -42, -42, -14, 1, 1, 26, 182, -546, -546, 182, 26, 1, 1, 178, -2314, 16198, -48594, 16198, -2314, 178, 1, 1, 90, -8010, -104130, 728910, 728910, -104130, -8010, 90, 1, 1, -2382, 107190 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 0, 6, 4, 2, -152, -674, -20468, 1233722, 556704368,...}.

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..57.

FORMULA

q=2;m=1;

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, -2, 1},

{1, 2, 2, 1},

{1, 2, -2, 2, 1},

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

{1, -14, -42, -42, -42, -14, 1},

{1, 26, 182, -546, -546, 182, 26, 1},

{1, 178, -2314, 16198, -48594, 16198, -2314, 178, 1},

{1, 90, -8010, -104130, 728910, 728910, -104130, -8010, 90, 1},

{1, -2382, 107190, 9539910, 124018830, 289377270, 124018830, 9539910, 107190, -2382, 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: A143187 A143209 A163994 * A206498 A184848 A184720

Adjacent sequences:  A156590 A156591 A156592 * A156594 A156595 A156596

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 10 2009

STATUS

approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)