A153879 A triangular sequence recursion: A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (5 (-2 + n) (-7 + 5 n))*A(n - 2, k - 1).

2, 5, 5, 2, 96, 2, 2, 748, 748, 2, 2, 1290, 27416, 1290, 2, 2, 2212, 372786, 372786, 2212, 2, 2, 3614, 1277998, 19936772, 1277998, 3614, 2, 2, 5596, 3471492, 390272910, 390272910, 3471492, 5596, 2, 2, 8258, 8283708, 2093481742, 27296452580

Offset

1,1

Comments

Row sums are:2*Product[5*k + 5, {k, 0, n - 1}]; {2, 10, 100, 1500, 30000, 750000, 22500000, 787500000, 31500000000,

1417500000000, 70875000000000, 3898125000000000}.

Links

Table of n, a(n) for n=1..41.

Formula

A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (5 (-2 + n) (-7 + 5 n))*A(n - 2, k - 1).

Example

{2},
{5, 5},
{2, 96, 2},
{2, 748, 748, 2},
{2, 1290, 27416, 1290, 2},
{2, 2212, 372786, 372786, 2212, 2},
{2, 3614, 1277998, 19936772, 1277998, 3614,2},
{2, 5596, 3471492, 390272910, 390272910, 3471492, 5596, 2},
{2, 8258, 8283708, 2093481742, 27296452580, 2093481742, 8283708, 8258, 2},
{2, 11700, 17917086, 8072731690, 700659339522, 700659339522, 8072731690, 17917086, 11700,2},
{2, 16022, 35766066, 25983458056, 5230652633932, 60361656251844, 5230652633932, 25983458056, 35766066, 16022, 2},
{2, 21324, 66787088, 73499502022, 26649375070488, 1922339558619076, 1922339558619076, 26649375070488, 73499502022, 66787088, 21324, 2}

Mathematica

A[1, 1] = 2; A[2, 1] := A[2, 2] = 5; A[3, 2] = 100 - 4;
A[4, 2] = 1500/2 - 2; A[4, 3] = 1500/2 - 2; A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (5 (-2 + n) (-7 + 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: A153648 A153354 A153821 * A074250 A161013 A115522

Adjacent sequences: A153876 A153877 A153878 * A153880 A153881 A153882

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 03 2009

Status

approved