0,5

Row sums are:

{1, 2, 12, 80, 728, 7912, 102640, 1528712, 25903216, 489632080, 10250405568,...}.

Tent even function:f(n,k)=If[k <= Floor[n/2], 2*k, 2*(n - k)];

Recursion function:m=2;

A(n,k,m)= ( m*(n - k) + 1)*A(n - 1, k - 1, m) +

(m*k + 1)*A( n - 1, k, m) +

m*f(n, k)*A(n - 2, k - 1, m).

{1},

{1, 1},

{1, 10, 1},

{1, 39, 39, 1},

{1, 128, 470, 128, 1},

{1, 397, 3558, 3558, 397, 1},

{1, 1206, 22387, 55452, 22387, 1206, 1},

{1, 3635, 128377, 632343, 632343, 128377, 3635, 1},

{1, 10924, 698788, 6107192, 12269406, 6107192, 698788, 10924, 1},

{1, 32793, 3686880, 53375112, 187721254, 187721254, 53375112, 3686880, 32793, 1},

{1, 98402, 19079273, 437314440, 2481082814, 4375255708, 2481082814, 437314440, 19079273, 98402, 1}

Clear[A, f, n, k, m];

f[n_, k_] := If[k <= Floor[n/2], 2*k, 2*(n - k)];

A[n_, 0, m_] := 1; A[n_, n_, m_] := 1;

A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m*k + 1)*A[n - 1, k, m] + m*f[n, k]*A[n - 2, k - 1, m];

Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];

Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]

Table[Table[Sum[A[n, k, m], {k, 0, n}], {n, 0, 10}], {m, 0, 10}];

Sequence in context: A146765 A154984 A008958 this_sequence A157629 A154336 A152971

Adjacent sequences: A157274 A157275 A157276 this_sequence A157278 A157279 A157280

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 26 2009