A156593 Triangle: 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])].

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

Offset

0,5

Links

Table of n, a(n) for n=0..57.

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: A143209 A163994 A355802 * A206498 A184848 A184720

Adjacent sequences: A156590 A156591 A156592 * A156594 A156595 A156596

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Feb 10 2009

Status

approved