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A142472 Triangle read by rows: t(n,m)=Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}]. 0
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; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are: {1, -3, 4, 53, -809, 7537, -41418, -294411, 15463669, -352665269, ...}.

LINKS

Table of n, a(n) for n=1..43.

FORMULA

t(n,m)=Binomial[n, m]*Sum[StirlingS1[n, k]*StirlingS1[k, m], {k, m, n}].

EXAMPLE

{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}

MATHEMATICA

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[%]

CROSSREFS

Cf. A039814.

Sequence in context: A126457 A159841 A202550 * A299445 A135049 A113384

Adjacent sequences:  A142469 A142470 A142471 * A142473 A142474 A142475

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 22 2008

EXTENSIONS

Edited by N. J. A. Sloane, Sep 26 2008

STATUS

approved

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Last modified July 11 05:49 EDT 2020. Contains 335609 sequences. (Running on oeis4.)