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A185876
Fourth accumulation array of A051340, by antidiagonals.
5
1, 5, 6, 15, 29, 21, 35, 85, 99, 56, 70, 195, 285, 259, 126, 126, 385, 645, 735, 574, 252, 210, 686, 1260, 1645, 1610, 1134, 462, 330, 1134, 2226, 3185, 3570, 3150, 2058, 792, 495, 1770, 3654, 5586, 6860, 6930, 5670, 3498, 1287, 715, 2640, 5670, 9114, 11956, 13230, 12390, 9570, 5643, 2002, 1001, 3795, 8415, 14070
OFFSET
1,2
COMMENTS
A member of the accumulation chain A051340 < A141419 < A185874 < A185875 < A185876 < ... (See A144112 for the definition of accumulation array.)
LINKS
FORMULA
T(n,k) = (4*n+5*k+11)*C(k+2,3)*C(n+4,4)/20, k>=1, n>=1.
EXAMPLE
Northwest corner:
1, 5, 15, 35, 70
6, 29, 85, 195, 385
21, 99, 285, 645, 1260
56, 259, 735, 1645, 3185
MATHEMATICA
f[n_, k_]:=k(1+k)n(1+n)(2+n)(5+4k+3n)/144;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185875 *)
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}]; (* accumulation array of {f(n, k)} *)
Factor[s[n, k]] (* formula for A185876 *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185876 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
CROSSREFS
Row 1: A000332, column 1: A000389.
Sequence in context: A115908 A247962 A241307 * A356496 A091020 A019070
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 05 2011
STATUS
approved