A174553 Triangle read by rows:t(n,m)=Sum[StirlingS2[n, k]*Eulerian[n - k + 1, m]*(-1)^(n - k - m)*k!, {k, 0, n}]

1, 1, 1, 1, 2, 1, 1, -9, 3, 1, 1, -56, -114, 4, 1, 1, -55, -590, -770, 5, 1, 1, 426, 6735, -2920, -4185, 6, 1, 1, -245, 47733, 216923, -2653, -20391, 7, 1, 1, -16372, -451052, 562016, 4011910, 109676, -93212, 8, 1, 1, -1011, -2697444, -49492896, -15614034

Offset

0,5

Comments

Row sums are:

{1, 2, 4, -4, -164, -1408, 64, 241376, 4122976, -8411008,...}.

Links

Table of n, a(n) for n=0..49.

Formula

t(n,m)=Sum[StirlingS2[n, k]*Eulerian[n - k + 1, m]*(-1)^(n - k - m)*k!, {k, 0, n}]

Example

{1},
{1, 1},
{1, 2, 1},
{1, -9, 3, 1},
{1, -56, -114, 4, 1},
{1, -55, -590, -770, 5, 1},
{1, 426, 6735, -2920, -4185, 6, 1},
{1, -245, 47733, 216923, -2653, -20391, 7, 1},
{1, -16372, -451052, 562016, 4011910, 109676, -93212, 8, 1},
{1, -1011, -2697444, -49492896, -15614034, 58337946, 1465644, -409224, 9, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_] = Sum[StirlingS2[n, k]*Eulerian[n - k + 1, m]*(-1)^( n - k - m)*k!, {k, 0, n}];
Table[Table[t[n, m], {m, 0, n - 1}], {n, 1, 10}];
Flatten[%]

Crossrefs

Sequence in context: A260374 A157109 A185814 * A167015 A124522 A016540

Adjacent sequences: A174550 A174551 A174552 * A174554 A174555 A174556

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 22 2010

Status

approved