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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A member of the accumulation chain A051340 < A141419 < A185874 < A185875 < A185876 < ... (See A144112 for the definition of accumulation array.)

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Johann Cigler, Some elementary observations on Narayana polynomials and related topics, arXiv:1611.05252 [math.CO], 2016. See p. 24.

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

Cf. A051340, A141419, A144112, A185874, A185875.

Row 1: A000332, column 1: A000389.

Sequence in context: A115908 A247962 A241307 * A091020 A019070 A019071

Adjacent sequences:  A185873 A185874 A185875 * A185877 A185878 A185879

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 05 2011

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)