0,5

Row sums are:

{1, 2, 8, 36, 208, 1388, 10796, 94340, 924308, 9960088, 117683872,...}.

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

Recursion function: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).

{1},

{1, 1},

{1, 6, 1},

{1, 17, 17, 1},

{1, 40, 126, 40, 1},

{1, 87, 606, 606, 87, 1},

{1, 182, 2413, 5604, 2413, 182, 1},

{1, 373, 8679, 38117, 38117, 8679, 373, 1},

{1, 756, 29376, 219020, 426002, 219020, 29376, 756, 1},

{1, 1523, 95668, 1133786, 3749066, 3749066, 1133786, 95668, 1523, 1},

{1, 3058, 303735, 5476744, 28433992, 49248812, 28433992, 5476744, 303735, 3058, 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: A119726 A103999 A154985 this_sequence A157268 A146959 A157632

Adjacent sequences: A157272 A157273 A157274 this_sequence A157276 A157277 A157278

nonn,tabl,uned

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