A156534 A triangular recursion sequence: A(n,k,m)= (m* n - m*k + 1)*A(n - 1, k - 1, m) + (m*k - (m - 1))*A(n - 1, k, m); t(n,k)=2*A(n, k, 1)*A(n + 1, k + 1, 0)/(n - k + 1) - A(n, k, 0)*A(n, k, 1).

1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 44, 26, 1, 1, 57, 0, 0, 57, 1, 1, 120, -1191, -6040, -1191, 120, 1, 1, 247, -10017, -109333, -109333, -10017, 247, 1, 1, 502, -58432, -1235276, -3061324, -1235276, -58432, 502, 1, 1, 1013, -287040, -10924608

Offset

1,5

Comments

Row sums are:

{1, 2, 6, 24, 98, 116, -8180, -238204, -5647734, -132491004,...}.

Links

Table of n, a(n) for n=1..49.

Formula

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

t(n,k)=2*A(n, k, 1)*A(n + 1, k + 1, 0)/(n - k + 1) - A(n, k, 0)*A(n, k, 1).

Example

{1},
{1, 1},
{1, 4, 1},
{1, 11, 11, 1},
{1, 26, 44, 26, 1},
{1, 57, 0, 0, 57, 1},
{1, 120, -1191, -6040, -1191, 120, 1},
{1, 247, -10017, -109333, -109333, -10017, 247, 1},
{1, 502, -58432, -1235276, -3061324, -1235276, -58432, 502, 1},
{1, 1013, -287040, -10924608, -55034868, -55034868, -10924608, -287040, 1013, 1}

Mathematica

Clear[A, n, k, m, e];
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];
Table[Table[2*A[n, k, 1]*A[n + 1, k + 1, 0]/(n - k + 1) - A[n, k, 0]*A[n, k, 1], {k, 1, n}], {n, 10}];
Flatten[%]

Crossrefs

Sequence in context: A154986 A154983 A324916 * A375858 A168287 A221987

Adjacent sequences: A156531 A156532 A156533 * A156535 A156536 A156537

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Feb 09 2009

Status

approved