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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 September 22 06:53 EDT 2020. Contains 337289 sequences. (Running on oeis4.)