A174587 - OEIS

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A174587

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

1, 1, 1, 1, 3, 1, 1, 49, 49, 1, 1, 553, 801, 553, 1, 1, -11999, -9839, -9839, -11999, 1, 1, -1125919, -1374463, -1376351, -1374463, -1125919, 1, 1, -25622015, -41341439, -44792831, -44792831, -41341439, -25622015, 1, 1, 3235358337, 3370753537

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

Row sums are:

1, 2, 5, 100, 1909, -43674, -6377113, -223512568, 22735136265, 4265143649290,

148391121390731,...

LINKS

Table of n, a(n) for n=0..38.

FORMULA

t(n,m)=If[n == 0, 1, Sum[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, 3, 1},

{1, 49, 49, 1},

{1, 553, 801, 553, 1},

{1, -11999, -9839, -9839, -11999, 1},

{1, -1125919, -1374463, -1376351, -1374463, -1125919, 1},

{1, -25622015, -41341439, -44792831, -44792831, -41341439, -25622015, 1},

{1, 3235358337, 3370753537, 3187620481, 3147671553, 3187620481, 3370753537, 3235358337, 1},

{1, 437895275521, 556690955521, 569908535041, 568077058561, 568077058561, 569908535041, 556690955521, 437895275521, 1},

{1, 7157082826369, 16706096371713, 19892759440513, 20296689312769, 20285865488001, 20296689312769, 19892759440513, 16706096371713, 7157082826369, 1}

MATHEMATICA

<< DiscreteMath`Combinatorica`

t[n_, m_] = If[n == 0, 1, Sum[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: A156727 A173505 A253178 * A177848 A168549 A010272

Adjacent sequences: A174584 A174585 A174586 * A174588 A174589 A174590

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 23 2010

STATUS

approved