1,1

Row sums are:

{3, 10, 45, 238, 1386, 8580, 55341, 367510, 2494206, 17215900,...}.

m = 0; p = 2; q = 1;

a(n,k)=(m*n - m*k + 1)*a(n - 1, k - 1) + (m*k - (m - 1))*a(n - 1, k);

f(n) = Product[k + 1, {k, 0, n}];

a0(n,m) = f[n]/(f[m]*f[n - m]);

t(n,k)=(p^(n - m)*q^m + p^m*q^(n - m))*a0(n - 1, k - 1)*a(n, k).

{3},

{5, 5},

{9, 27, 9},

{17, 102, 102, 17},

{33, 330, 660, 330, 33},

{65, 975, 3250, 3250, 975, 65},

{129, 2709, 13545, 22575, 13545, 2709, 129},

{257, 7196, 50372, 125930, 125930, 50372, 7196, 257},

{513, 18468, 172368, 603288, 904932, 603288, 172368, 18468, 513},

{1025, 46125, 553500, 2583000, 5424300, 5424300, 2583000, 553500, 46125, 1025}

Clear[A, a0, b0, n, k, m];

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

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

f[n_] = Product[k + 1, {k, 0, n}]; a0[n_, m_] = f[n]/(f[m]*f[n - m]); ;

m = 0; p = 2; q = 1;

Table[(p^(n - m)*q^m + p^m*q^(n - m))*a0[n - 1, k - 1]*A[n, k, m], {n, 10}, {k, n}];

Flatten[%]

A001263

Sequence in context: A120841 A145282 A049757 this_sequence A164663 A098971 A093572

Adjacent sequences: A155534 A155535 A155536 this_sequence A155538 A155539 A155540

nonn,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 23 2009