A156594 Triangle: q=3; m=2; 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, -3, 1, 1, 6, 6, 1, 1, -3, 6, -3, 1, 1, -21, -21, -21, -21, 1, 1, 24, 168, -84, 168, 24, 1, 1, 195, -1560, 5460, 5460, -1560, 195, 1, 1, -111, 7215, 28860, 202020, 28860, 7215, -111, 1, 1, -3072, -113664, -3694080, 29552640, 29552640, -3694080

Offset

0,5

Links

Table of n, a(n) for n=0..51.

Example

{1},
{1, 1},
{1, -3, 1},
{1, 6, 6, 1},
{1, -3, 6, -3, 1},
{1, -21, -21, -21, -21, 1},
{1, 24, 168, -84, 168, 24, 1},
{1, 195, -1560, 5460, 5460, -1560, 195, 1},
{1, -111, 7215, 28860, 202020, 28860, 7215, -111, 1},
{1, -3072, -113664, -3694080, 29552640, 29552640, -3694080, -113664, -3072, 1},
{1, -4053, -4150272, 76780032, -4990702080, 5703659520, -4990702080, 76780032, -4150272, -4053, 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: A190907 A035582 A370420 * A109647 A176668 A054120

Adjacent sequences: A156591 A156592 A156593 * A156595 A156596 A156597

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Feb 10 2009

Status

approved