A153782 A recursive triangular sequence with row sums (5^(n - 1)*(n + 3)!): A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + 5 *(2 + n) (13 + 5* n)*A(n - 2, k - 1).

24, 300, 300, 2, 17996, 2, 2, 314998, 314998, 2, 2, 317660, 24564676, 317660, 2, 2, 321102, 566678896, 566678896, 321102, 2, 2, 325424, 1253145598, 54193057952, 1253145598, 325424, 2, 2, 330726, 2104391322, 1557145277950, 1557145277950

Offset

1,1

Comments

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

{24, 600, 18000, 630000, 25200000, 1134000000, 56700000000, 3118500000000,

187110000000000, 12162150000000000, 851350500000000000, 63851287500000000000,...}

Links

Table of n, a(n) for n=1..33.

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

{24},
{300, 300},
{2, 17996, 2},
{2, 314998, 314998, 2},
{2, 317660, 24564676, 317660, 2},
{2, 321102, 566678896, 566678896, 321102, 2},
{2, 325424, 1253145598, 54193057952, 1253145598, 325424, 2},
{2, 330726, 2104391322, 1557145277950, 1557145277950, 2104391322, 330726, 2},
{2, 337108, 3142824608, 5556784126892, 175990145422780, 5556784126892, 3142824608, 337108, 2},
{2, 344670, 4393305996, 13514526148660, 6067556080200672, 6067556080200672, 13514526148660, 4393305996, 344670, 2},
{2, 353512, 5883668026, 27410204222016, 30642056447211972, 790011554929088944, 30642056447211972, 27410204222016, 5883668026, 353512, 2},
{2, 363734, 7645285238, 49865881529602, 99728695271086588, 31825865181201734836, 31825865181201734836, 99728695271086588, 49865881529602, 7645285238, 363734, 2}

Mathematica

Clear[A]; A[1, 1] = 24; A[2, 1] := A[2, 2] = 5* 60;
A[3, 2] = 18000 - 4; A[4, 2] = 630000/2 - 2; A[4, 3] = 630000/2 - 2;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + 5 *(2 + n) (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: A161524 A161931 A162366 * A073990 A056290 A056285

Adjacent sequences: A153779 A153780 A153781 * A153783 A153784 A153785

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Jan 01 2009

Status

approved