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.

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.)

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

Cf. A144112, A185730.

Sequence in context: A203976 A213566 A143129 * A177765 A367965 A337122

Adjacent sequences: A185728 A185729 A185730 * A185732 A185733 A185734

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 01 2011

Status

approved