OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(n,k) = F*(k*n-n+3*k+13), where F = k*(k+1)*(k+2)*n*(n+1)*(n+2)/576.
EXAMPLE
Northwest corner:
1.....5....15....35....70
4.....21...65....155...315
10....55...175...425...875
20....115..375...925...1925
MATHEMATICA
f[n_, k_]:=k(1+k)n(1+n)(7+2k-n+k*n)/36;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185730 *)
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* acc. arr. of {f(n, k)} *)
Factor[s[n, k]] (* formula for A185731 *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185731 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten (* A185731 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 01 2011
STATUS
approved