sum((i-a)!*(i-b)!*(i-c)!/((i+a+1)!*(i+b+1)!*(i+c+1)!),i,0,inf) =((-a-1)!*(-b-1)!*(-c-1)!/2)*(((c+b+a)!/((b+a)!*(c+a)!*(c+b)!))-1/(a!*b!*c!)) inf ==== \ (i - a)! (i - b)! (i - c)!
-------------------------------------- = / (i + a + 1)! (i + b + 1)! (i + c + 1)! ==== i = 0
(- a - 1)! (- b - 1)! (- c - 1)! (c + b + a)! 1 -------------------------------- (-------------------------- - --------). 2 (b + a)! (c + a)! (c + b)! a! b! c! E.g., (c78) minfactorial(limit(subst([c = a,b = a],%),a,0)) inf ==== \ 1 (d78) > -------- = zeta(3) / 3 ==== (i + 1) i = 0 Looks like there's a bilateral version, too. --rwg PS: An easy sudoku with a blank row, (auto)morphed from 18 Nov LIFE "magazine": [[8,3,_;_,_,1;9,_,_],[_,7,_;8,4,_;_,_,_],[_,_,6;_,9,_;_,1,3]; [7,9,_;_,_,_;_,_,_],[1,_,_;_,_,_;_,_,2],[_,_,_;_,_,_;_,3,4]; [4,5,_;_,7,_;2,_,_],[_,_,_;_,6,4;_,8,_],[_,_,8;9,_,_;_,7,5]] [ [ 8 3 _ ] [ _ 7 _ ] [ _ _ 6 ] ] [ [ ] [ ] [ ] ] [ [ _ _ 1 ] [ 8 4 _ ] [ _ 9 _ ] ] [ [ ] [ ] [ ] ] [ [ 9 _ _ ] [ _ _ _ ] [ _ 1 3 ] ] [ ] [ [ 7 9 _ ] [ 1 _ _ ] [ _ _ _ ] ] [ [ ] [ ] [ ] ] [ [ _ _ _ ] [ _ _ _ ] [ _ _ _ ] ] [ [ ] [ ] [ ] ] [ [ _ _ _ ] [ _ _ 2 ] [ _ 3 4 ] ] [ ] [ [ 4 5 _ ] [ _ _ _ ] [ _ _ 8 ] ] [ [ ] [ ] [ ] ] [ [ _ 7 _ ] [ _ 6 4 ] [ 9 _ _ ] ] [ [ ] [ ] [ ] ] [ [ 2 _ _ ] [ _ 8 _ ] [ _ 7 5 ] ]