A153878 A triangular sequence recursion: A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (-12 + 5 n) (-9 + 5 n)*A(n - 2, k - 1).

2, 3, 3, 2, 44, 2, 2, 310, 310, 2, 2, 728, 9772, 728, 2, 2, 1486, 127680, 127680, 1486, 2, 2, 2684, 564510, 6099016, 564510, 2684, 2, 2, 4422, 1857042, 117489766, 117489766, 1857042, 4422, 2, 2, 6800, 5050056, 789984688, 7480610540, 789984688, 5050056

Offset

1,1

Comments

Row sums are:2*Product[5*k + 3, {k, 0, n - 1}];

{2, 6, 48, 624, 11232, 258336, 7233408, 238702464, 9070693632, 390039826176,

18721911656448, 992261317791744,...}.

Links

Table of n, a(n) for n=1..43.

Formula

A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (-12 + 5 n) (-9 + 5 n)*A(n - 2, k - 1).

Example

{2},
{3, 3},
{2, 44, 2},
{2, 310, 310, 2},
{2, 728, 9772, 728, 2},
{2, 1486, 127680, 127680, 1486, 2},
{2, 2684, 564510, 6099016, 564510, 2684, 2},
{2, 4422, 1857042, 117489766, 117489766, 1857042, 4422, 2},
{2, 6800, 5050056, 789984688, 7480610540, 789984688, 5050056, 6800, 2},
{2, 9918, 11946332, 3688306180, 191319650656, 191319650656, 3688306180, 11946332, 9918, 2},
{2, 13876, 25406650, 13689263280, 1757597669700, 15179286949432, 1757597669700, 13689263280, 25406650, 13876, 2},
{2, 18774, 49699790, 42959290666, 10800260461620, 485287389425020, 485287389425020, 10800260461620, 42959290666, 49699790, 18774, 2}

Mathematica

A[1, 1] = 2; A[2, 1] := A[2, 2] = 3;
A[3, 2] = 48 - 4; A[4, 2] = 624/2 - 2; A[4, 3] = 624/2 - 2;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (-12 + 5 n) (-9 + 5 n)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 12}, {k, n}]; Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 12}];

Crossrefs

Sequence in context: A215490 A153592 A351188 * A118925 A308100 A351065

Adjacent sequences: A153875 A153876 A153877 * A153879 A153880 A153881

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 03 2009

Status

approved