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A156593
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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])].
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0
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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
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OFFSET
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0,5
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..57.
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FORMULA
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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])].
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EXAMPLE
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{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}
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A143187 A143209 A163994 * A206498 A184848 A184720
Adjacent sequences: A156590 A156591 A156592 * A156594 A156595 A156596
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KEYWORD
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sign,tabl,uned
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AUTHOR
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Roger L. Bagula, Feb 10 2009
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STATUS
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approved
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