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 A185507 Second accumulation array, T, of the natural number array A000027, by antidiagonals. 5
 1, 4, 5, 11, 19, 15, 25, 49, 55, 35, 50, 105, 136, 125, 70, 91, 200, 280, 300, 245, 126, 154, 350, 515, 600, 575, 434, 210, 246, 574, 875, 1075, 1125, 1001, 714, 330, 375, 894, 1400, 1785, 1975, 1925, 1624, 1110, 495, 550, 1335, 2136, 2800, 3220, 3325, 3080, 2496, 1650, 715, 781, 1925, 3135, 4200, 4970, 5341, 5250, 4680, 3675, 2365, 1001, 1079, 2695, 4455, 6075, 7350, 8134, 8330, 7890, 6825, 5225, 3289, 1365, 1456, 3679, 6160, 8525, 10500, 11886, 12544, 12390, 11400, 9625, 7216, 4459, 1820, 1925, 4914, 8320, 11660 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A144112 (and A185506) for the definition of accumulation array (aa). Sequence is aa(aa(A000027)). LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n,k) = k*n*(k+1)*(n+1)*(3*n^2 + (4*k+11)*n + 3*k^2 - k + 16)/144. EXAMPLE Northwest corner:    1,   4,  11,   25,   50,   91,  154    5,  19,  49,  105,  200,  350,  574   15,  55, 136,  280,  515,  875, 1400   35, 125, 300,  600, 1075, 1785, 2800   70, 245, 575, 1125, 1975, 3220, 4970 MATHEMATICA g[n_, k_]:=k*n(k+1)(n+1)(3n^2+(4k+11)n+3k^2-k+16)/144; TableForm[Table[g[n, k], {n, 1, 10}, {k, 1, 15}]] Table[g[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten CROSSREFS Cf. A006522 (row 1), A000332 (column 1). Cf. A000027, A185506, A185508, A185509. Sequence in context: A118143 A001350 A077238 * A000286 A227620 A036539 Adjacent sequences:  A185504 A185505 A185506 * A185508 A185509 A185510 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 29 2011 STATUS approved

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Last modified April 23 12:15 EDT 2021. Contains 343204 sequences. (Running on oeis4.)