A090435 Triangle of signed numbers used for the computation of the column sequences of triangle A090217.

1, -1, 6, 1, -48, 147, -5, 1584, -24255, 50176, 1, -1980, 121275, -1003520, 1571724, -41, 496980, -113458275, 2950635520, -16174611684, 20412000000, 45182, -3322062810, 2744728561050, -206756932157440, 3081396966348393, -12443694076800000, 13160600037440625, -1294492177294

Offset

1,3

Comments

A090217(n+m,m)= sum(a(m,p)*((p+4)*(p+3)*(p+2)*(p+1)*p)^n,p=1..m)/D(m) with D(m) := A090436(m); m=1,2,..., n>=0.

Links

Table of n, a(n) for n=1..29.

W. Lang, First 8 rows.

Formula

a(n, m)= D(n)*((-1)^(n-m))*(fallfac(m+4, 5)^(n-1))/(product(fallfac(m+4, 5)-fallfac(r+4, 5), r=1..m-1)*product(fallfac(r+4, 5)-fallfac(m+4, 5), r=m+1..n)), with D(n) := A090436(n) and fallfac(n, m) := A008279(n, m) (falling factorials), 1<=m<=n else 0. (Replace in the denominator the first product by 1 if m=1 and the second one by 1 if m=n.)

Example

[1]; [ -1,6]; [1,-48,147]; [ -5,1584,-24255,50176]; ...
A090217(2+3,3) = 9086400 = (1*(5*4*3*2*1)^2 - 48*(6*5*4*3*2)^2 + 147*(7*6*5*4*3)^2)/100.
a(3,2)= -48 = 100*(-1)*((6*5*4*3*2)^2)/((6*5*4*3*2-5*4*3*2*1)*(7*6*5*4*3-6*5*4*3*2)).

Crossrefs

Sequence in context: A113392 A113387 A290316 * A136237 A308281 A347211

Adjacent sequences: A090432 A090433 A090434 * A090436 A090437 A090438

Keyword

sign,easy,tabl

Author

Wolfdieter Lang, Dec 01 2003

Status

approved