A153811 A recursive triangular sequence with row sums (5^(n - 1)*(n + 3)!)/12: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + 5 *(2 + n) (13 + 5* n)*A(n - 2, k - 1).

2, 25, 25, 2, 1496, 2, 2, 26248, 26248, 2, 2, 28910, 2042176, 28910, 2, 2, 32352, 47217646, 47217646, 32352, 2, 2, 36674, 109695598, 4505535452, 109695598, 36674, 2, 2, 41976, 195465072, 129741992950, 129741992950, 195465072, 41976, 2, 2

Offset

1,1

Comments

Row sums are:(5^(n - 1)*(n + 3)!)/12:

{2, 50, 1500, 52500, 2100000, 94500000, 4725000000, 259875000000,

15592500000000, 1013512500000000, 70945875000000000, 5320940625000000000,...}.

The whole sequence is adjusted to get the lowest terms.

Links

Table of n, a(n) for n=1..37.

Formula

A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + 5 *(2 + n) (13 + 5* n)*A(n - 2, k - 1).

Example

{2},
{25, 25},
{2, 1496, 2},
{2, 26248, 26248, 2},
{2, 28910, 2042176, 28910, 2},
{2, 32352, 47217646, 47217646, 32352, 2},
{2, 36674, 109695598, 4505535452, 109695598, 36674, 2},
{2, 41976, 195465072, 129741992950, 129741992950, 195465072, 41976, 2},
{2, 48358, 312497108, 479866415642, 14632142077780, 479866415642, 312497108, 48358, 2},
{2, 55920, 471214746, 1219036884910, 505536741844422, 505536741844422, 1219036884910, 471214746, 55920, 2},
{2, 64762, 685013026, 2600745317016, 2627765335866972, 65685141467476444, 2627765335866972, 2600745317016, 685013026, 64762, 2},
{2, 74984, 970828988, 5009337682102, 8859644563074088, 2651605657628339836, 2651605657628339836, 8859644563074088, 5009337682102, 970828988, 74984, 2}

Mathematica

Clear[A]; A[1, 1] = 2; A[2, 1] := A[2, 2] = 5* 60/12; A[3, 2] = (18000 - 48)/12; A[4, 2] = (630000/2 - 24)/12; A[4, 3] = (630000/2 - 24)/12; A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + 5 *(2 + n) (13 + 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}];
Table[Apply[Plus, a[[n]]]/(5^(n - 1)*(n + 3)!), {n, 1, 12}];

Crossrefs

Sequence in context: A161575 A036502 A076449 * A101962 A092045 A317886

Adjacent sequences: A153808 A153809 A153810 * A153812 A153813 A153814

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Jan 01 2009

Status

approved