This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090435 #9 Aug 29 2019 17:24:54 %S A090435 1,-1,6,1,-48,147,-5,1584,-24255,50176,1,-1980,121275,-1003520, %T A090435 1571724,-41,496980,-113458275,2950635520,-16174611684,20412000000, %U A090435 45182,-3322062810,2744728561050,-206756932157440,3081396966348393,-12443694076800000,13160600037440625,-1294492177294 %N A090435 Triangle of signed numbers used for the computation of the column sequences of triangle A090217. %C A090435 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. %H A090435 W. Lang, <a href="/A090435/a090435.txt">First 8 rows</a>. %F A090435 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.) %e A090435 [1]; [ -1,6]; [1,-48,147]; [ -5,1584,-24255,50176]; ... %e A090435 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. %e A090435 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)). %K A090435 sign,easy,tabl %O A090435 1,3 %A A090435 _Wolfdieter Lang_, Dec 01 2003