login
A185731
Array by antidiagonals: T(n,k)=F*(k*n-n+3*k+13), where F = k*(k+1)*(k+2)*n*(n+1)*(n+2)/576.
2
1, 5, 4, 15, 21, 10, 35, 65, 55, 20, 70, 155, 175, 115, 35, 126, 315, 425, 375, 210, 56, 210, 574, 875, 925, 700, 350, 84, 330, 966, 1610, 1925, 1750, 1190, 546, 120, 495, 1530, 2730, 3570, 3675, 3010, 1890, 810, 165, 715, 2310, 4350, 6090, 6860, 6370, 4830, 2850, 1155, 220, 1001, 3355, 6600
OFFSET
1,2
COMMENTS
This is the accumulation array of A185730. (See A144112 for the definition of accumulation array.)
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
Sequence in context: A203976 A213566 A143129 * A177765 A367965 A337122
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 01 2011
STATUS
approved