A174588 A symmetrical triangular sequence adjusted by -t[n,-1]+1 :t(n,m)=If[n == 0, 1, Sum[Binomial[n, k]*Eulerian[n + 1, k]*(-1)^k*(m + 1 - k)^n, {k, 0, n}]]

1, 1, 1, 1, 7, 1, 1, 181, 181, 1, 1, 751, 1761, 751, 1, 1, -323399, -354899, -354899, -323399, 1, 1, -20873579, -27315455, -27944027, -27315455, -20873579, 1, 1, 1429118713, 1312010281, 1219622545, 1219622545, 1312010281, 1429118713, 1, 1

Offset

0,5

Comments

Row sums are:

1, 2, 9, 364, 3265, -1356594, -124322093, 7921503080, 3867350839137,

254033305455610, -174275807582741689,...

Links

Table of n, a(n) for n=0..36.

Formula

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

out_n,m=t(n,m)-t(n,-1)+1

Example

{1},
{1, 1},
{1, 7, 1},
{1, 181, 181, 1},
{1, 751, 1761, 751, 1},
{1, -323399, -354899, -354899, -323399, 1},
{1, -20873579, -27315455, -27944027, -27315455, -20873579, 1},
{1, 1429118713, 1312010281, 1219622545, 1219622545, 1312010281, 1429118713, 1},
{1, 481723390135, 577653410305, 583205489911, 582186258433, 583205489911, 577653410305, 481723390135, 1},
{1, 19475791988401, 33530084432461, 36881727519781, 37129048787161, 37129048787161, 36881727519781, 33530084432461, 19475791988401, 1},
{1, -17832181758066323, -19958592533330175, -19793122506695075, -19704919818993023, -19698174348572499, -19704919818993023, -19793122506695075, -19958592533330175, -17832181758066323, 1}

Mathematica

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

Crossrefs

Sequence in context: A331899 A111830 A212943 * A366316 A199001 A350048

Adjacent sequences: A174585 A174586 A174587 * A174589 A174590 A174591

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 23 2010

Status

approved