Some Sum-Of-Sum Congruences
Ralf Stephan
ralf at ark.in-berlin.de
Wed Mar 3 09:03:39 CET 2004
> qqquet at mindspring.com (Leroy Quet) wrote in message
> For n>= 2,
>
> A(n,m) =
>
> (1/(n-1)!)*
> sum{k>=0} sum{j=1 to n-1} S(n-1,j)*(
> [m+1-6k]^j +[m-6k]^j -[m-2-6k]^j -[m-3-6k]^j),
>
> where S() is an unsigned Stirling number of the first kind,
> and [x] = maximum(0,x).
>
> I should also probably give the first few terms of A(n,m):
>
> A(0,m): 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0,...
> A(1,m): 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0,...
> A(2,m): 1, 3, 5, 6, 6, 6, 7, 9, 11, 12, 12, 12,...
> A(3,m): 1, 4, 9, 15, 21, 27, 34, 43, 54, 66, 78, 90,...
A(n+1,m) are partial sums of A(n,m), and the first three
are A010892, A021823, A077859.
ralf
More information about the SeqFan
mailing list