A090219 Signed triangle used to compute column sequences of array A078741 ((3,3)-Stirling2).
1, -1, 4, 1, -8, 10, -1, 12, -30, 20, 1, -64, 600, -1600, 1225, -1, 80, -1000, 4000, -6125, 3136, 1, -96, 1500, -8000, 18375, -18816, 7056, -1, 448, -21000, 280000, -1500625, 3687936, -4148928, 1728000, 1, -512, 28000, -448000, 3001250, -9834496, 16595712, -13824000, 4492125, -1
Offset: 3
Examples
The third (k=5) column sequence of array A078741 is A078741(n+3,5)=c(5; n)= b(3)*(1*(3*2*1)^n -8*(4*3*2)^n +10*(5*4*3)^n), with b(3)= N(3)/A090220(3)=3/1=3, n>=0. This is 9*A089518. The fifth (k=7) column sequence of array A078741 is A078741(n+3,7)=c(7; n)= b(5)*(1*(3*2*1)^n -64*(4*3*2)^n +600*(5*4*3)^n -1600*(6*5*4)^n +1225*(7*6*5)^n), with b(5)= N(5)/A090220(5)=3/2, n>=0. This is the sequence [243, 149580, 49658508, 13062960720,... ] which has a factor of 27. Triangle begins: [1]; [-1,4]; [1,-8,10]; [-1,12,-30,20]; [1,-64,600,-1600,1225]; ...
Links
- Wolfdieter Lang, First 10 rows.
Crossrefs
Companion sequence A090220 for denominators D(m).
Comments