A153737 A recursive triangular sequence with row sums (2*(n + 5)!): A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1).

2, 5040, 5040, 2, 80636, 2, 2, 362878, 362878, 2, 2, 363024, 6531548, 363024, 2, 2, 363206, 39553592, 39553592, 363206, 2, 2, 363428, 79849438, 797577464, 79849438, 363428, 2, 2, 363694, 128156058, 6098501046, 6098501046, 128156058, 363694, 2, 2

Offset

1,1

Comments

Row sums are (2*(n + 5)!) except for n=1:

{2, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600,

174356582400, 2615348736000}.

Links

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

Formula

A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + (n + 4)*(n + 3)*A(n - 2, k - 1).

Example

{2},
{5040, 5040},
{2, 80636, 2},
{2, 362878, 362878, 2},
{2, 363024, 6531548, 363024, 2},
{2, 363206, 39553592, 39553592, 363206, 2},
{2, 363428, 79849438, 797577464, 79849438, 363428, 2},
{2, 363694, 128156058, 6098501046, 6098501046, 128156058, 363694, 2},
{2, 364008, 185214520, 18683169432, 136619086476, 18683169432, 185214520, 364008, 2},
{2, 364374, 251770836, 42192786508, 1265229446280, 1265229446280, 42192786508, 251770836, 364374, 2}

Mathematica

Clear[A]; A[2, 1] := A[2, 2] = 7!;
A[3, 2] = 2*8! - 4; A[4, 2] = A[4, 3] = 9! - 2;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n + 4)*(n + 3)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 10}, {k, n}];
Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 10}]; |Q Table[Apply[Plus, a[[n]]]/(2*(n + 5)!), {n, 1, 10}];

Crossrefs

Sequence in context: A203756 A232712 A262059 * A078933 A064029 A057645

Adjacent sequences: A153734 A153735 A153736 * A153738 A153739 A153740

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 31 2008

Status

approved