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A157117 A triangular sequence: t0(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];(Eulerian); t(n,m)=If[m <= n, t0(n*m + 1, n - m), t0(n*(n - m) + 1, m]) + If[ - m + n <= n, t0(n (-m + n) + 1, n - (-m + n)), t0(n (n - (-m + n)) + 1, -m + n)]. 1
2, 1, 1, 1, 8, 1, 1, 131, 131, 1, 1, 8204, 29216, 8204, 1, 1, 2097187, 44136233, 44136233, 2097187, 1, 1, 2147483736, 846839476071, 503464582368, 846839476071, 2147483736, 1, 1, 8796093022411, 150092195453359483, 288159195861579519 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are;

{2, 2, 10, 264, 45626, 92466842, 2201438501984, 876520374815922828,

10374803176694228455176658, 2886866177138216211156046527897756,

19833869740132886286873186460130215759984532,...}

LINKS

Table of n, a(n) for n=0..31.

FORMULA

t0(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];

t(n,m)=If[m <= n, t0(n*m + 1, n - m), t0(n*(n - m) + 1, m]) +

If[ - m + n <= n, t0(n (-m + n) + 1, n - (-m + n)), t0(n (n - (-m + n)) + 1, -m + n)].

EXAMPLE

{2},

{1, 1},

{1, 8, 1},

{1, 131, 131, 1},

{1, 8204, 29216, 8204, 1},

{1, 2097187, 44136233, 44136233, 2097187, 1},

{1, 2147483736, 846839476071, 503464582368, 846839476071, 2147483736, 1},

{1, 8796093022411, 150092195453359483, 288159195861579519, 288159195861579519, 150092195453359483, 8796093022411, 1},

{1, 144115188075856316, 239299301114175511474096, 4834192459903264655728316, 227819366428971969059200, 4834192459903264655728316, 239299301114175511474096, 144115188075856316, 1},

{1, 9444732965739290428331, 3433683819093485605511363245745, 1298064445774707016553225940889226, 141934958965862870453546669385575, 141934958965862870453546669385575, 1298064445774707016553225940889226, 3433683819093485605511363245745, 9444732965739290428331, 1},

{1, 2475880078570760549798250392, 443426488242839506118951852148371693230, 5575185758951072202571914302091772690354288, 4336479082877678057396108985080155821025155, 9653203498895136164744840560962397338400, 4336479082877678057396108985080155821025155, 5575185758951072202571914302091772690354288, 443426488242839506118951852148371693230, 2475880078570760549798250392, 1}

MATHEMATICA

Clear[t, n, m];

t0[n_, k_] := Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}];

t[n_, m_] = If[m <= n, t0[n*m + 1, n - m], t0[n*(n - m) +

1, m]] + If[ -m + n <= n, t0[n (- m + n) + 1, n - (-m + n)], t0[n (n - (-m + n)) + 1, -m + n]];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A329043 A329042 A171660 * A322143 A264081 A061538

Adjacent sequences:  A157114 A157115 A157116 * A157118 A157119 A157120

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 23 2009

STATUS

approved

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Last modified September 29 14:39 EDT 2020. Contains 337432 sequences. (Running on oeis4.)