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A142472
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Triangle read by rows: t(n,m)=Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}].
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0
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1, -4, 1, 21, -18, 1, -140, 240, -48, 1, 1140, -3150, 1300, -100, 1, -11004, 43620, -29700, 4800, -180, 1, 123074, -650769, 647780, -175175, 13965, -294, 1, -1566928, 10517108, -14190400, 5676160, -764400, 34496, -448, 1, 22390488, -184052520, 319680732, -175091112, 35160048, -2698920, 75600
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Row sums are: {1, -3, 4, 53, -809, 7537, -41418, -294411, 15463669, -352665269, ...}.
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LINKS
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Table of n, a(n) for n=1..43.
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FORMULA
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t(n,m)=Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}].
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EXAMPLE
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{1},
{-4, 1},
{21, -18, 1},
{-140, 240, -48, 1},
{1140, -3150, 1300, -100, 1},
{-11004, 43620, -29700, 4800, -180, 1},
{123074, -650769,647780, -175175, 13965, -294, 1},
{-1566928, 10517108, -14190400, 5676160, -764400, 34496, -448, 1},
{22390488, -184052520, 319680732, -175091112, 35160048, -2698920, 75600, -648, 1},
{-354995760, 3478726080, -7492500000, 5330088750, -1475938800, 169943760, -8139600, 151200, -900, 1}
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MATHEMATICA
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t[n_, m_] = Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
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CROSSREFS
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Cf. A039814.
Sequence in context: A126457 A159841 A202550 * A299445 A135049 A113384
Adjacent sequences: A142469 A142470 A142471 * A142473 A142474 A142475
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KEYWORD
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sign,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, Sep 22 2008
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EXTENSIONS
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Edited by N. J. A. Sloane, Sep 26 2008
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STATUS
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approved
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