OFFSET
1,2
COMMENTS
The matrix inverse starts
1;
-2,1;
-2,-4,1;
1,0,-6,1;
7,10,6,-8,1;
16,14,19,16,-10,1;
28,0,-3,20,30,-12,1;
43,-35,-60,-52,5,48,-14,1;
61,-76,-89,-112,-125,-34,70,-16,1; - R. J. Mathar, Mar 22 2013
FORMULA
T(n,m)=sum(i=m..n, i*(-1)^(i-m) *binomial(i-1,m-1) *sum(k=0..n-i, binomial(k,n-k-i) *3^k *(-1)^(n-k-i) *binomial(n+k-1,n-1)))/n.
EXAMPLE
1
2, 1,
10, 4, 1,
59, 24, 6, 1,
385, 158, 42, 8, 1,
2672, 1106, 305, 64, 10, 1,
19336, 8064, 2283, 508, 90, 12, 1
MAPLE
A202483 := proc(n, m)
if m < 1 or m > n then
0;
else
a := 0 ;
for i from m to n do
a := a+ i*(-1)^(i-m)*binomial(i-1, m-1) *add( binomial(k, n-k-i) *3^k *(-1)^(n-k-i) *binomial(n+k-1, n-1), k=0..n-i) ;
end do:
return a/n ;
end if;
end proc: # R. J. Mathar, Mar 22 2013
PROG
(Maxima)
T(n, m):=sum(i*(-1)^(i-m)*binomial(i-1, m-1)*sum(binomial(k, n-k-i)*3^(k)*(-1)^(n-k-i)*binomial(n+k-1, n-1), k, 0, n-i), i, m, n)/n;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Dec 20 2011
STATUS
approved