A156233 A symmetrical recursion triangular sequence: m=4; e(n,k,m)= (2* k + m - 1)e(n - 1, k, m) + (m*n - 2*k + 1 - m)e(n - 1, k - 1, m); t(n,k)=e(n, k, m) + e(n, n - k, m).

2, 1, 1, 1, 6, 1, 1, 37, 37, 1, 1, 226, 606, 226, 1, 1, 1565, 7972, 7972, 1565, 1, 1, 13514, 102407, 187824, 102407, 13514, 1, 1, 150753, 1445555, 3859373, 3859373, 1445555, 150753, 1, 1, 2105142, 23789060, 79955452, 115641606, 79955452, 23789060

Offset

0,1

Comments

Row sums are:

{2, 2, 8, 76, 1060, 19076, 419668, 10911364, 327340916, 11129591140, 422924463316,...}.

Since m=2 is A060187, this recursion seems to be a MacMahon numbers level recursion.

Links

Table of n, a(n) for n=0..42.

Formula

m=4;e(n,k,m)= (2*k + m - 1)e)n - 1, k, m) + (m*n - 2*k + 1 - m)e(n - 1, k - 1, m);

t(n,k)=e(n, k, m) + e(n, n - k, m).

Example

{2},
{1, 1},
{1, 6, 1},
{1, 37, 37, 1},
{1, 226, 606, 226, 1},
{1, 1565, 7972, 7972, 1565, 1},
{1, 13514, 102407, 187824, 102407, 13514, 1},
{1, 150753, 1445555, 3859373, 3859373, 1445555, 150753, 1},
{1, 2105142, 23789060, 79955452, 115641606, 79955452, 23789060, 2105142, 1},
{1, 34850041, 457127618, 1813119912, 3259697998, 3259697998, 1813119912, 457127618, 34850041, 1},
{1, 656682190, 9977604269, 46096675274, 96031672538, 117399194772, 96031672538, 46096675274, 9977604269, 656682190, 1}

Mathematica

Clear[e, n, k, m]; m = 4; e[n_, 0, m_] := 1;
e[n_, k_, m_] := 0 /; k >= n; e[n_, k_, 1] := 1 /; k >= n;
e[n_, k_, m_] := (2*k + m - 1)e[n - 1, k, m] + (m*n - 2*k + 1 - m)e[n - 1, k - 1, m];
Table[Table[e[n, k, m], {k, 0, n - 1}], {n, 1, 10}];
Flatten[%];
Table[Table[e[n, k, m] + e[n, n - k, m], {k, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A060187.

Sequence in context: A280491 A157118 A156186 * A251725 A292977 A295381

Adjacent sequences: A156230 A156231 A156232 * A156234 A156235 A156236

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Feb 06 2009

Status

approved