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 A185509 Fourth accumulation array, T, of the natural number array A000027, by antidiagonals. 5
 1, 6, 7, 22, 41, 28, 63, 146, 161, 84, 154, 406, 561, 476, 210, 336, 966, 1526, 1631, 1176, 462, 672, 2058, 3556, 4361, 3976, 2562, 924, 1254, 4032, 7434, 9996, 10486, 8568, 5082, 1716, 2211, 7392, 14322, 20580, 23716, 22344, 16842, 9372, 3003, 3718, 12837, 25872, 39102, 48216, 49980, 43512, 30822, 16302, 5005, 6006, 21307, 44352, 69762, 90552, 100548, 96432, 79002, 53262, 27027, 8008, 9373, 34034, 72787, 118272, 159852 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A144112 (and A185506) for the definition of rectangular sum array (aa). Sequence is aa(aa(aa(aa(A000027)))). LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n,k) = F*(5*n^2 + (6*k + 39)*n + 5*k^2 + 9*k + 86), where F = k*(k+1)*(k+2)*(k+3)*n*(n+1)*(n+2)*(n+3)/86400. EXAMPLE Northwest corner: 1.....6....22....63...154 7....41...146...406...966 28..161...561..1526..3556 84..476..1631..4361..9996 MATHEMATICA u[n_, k_]:=k(k+1)(k+2)(k+3)n(n+1)(n+2)(n+3)(5n^2+(6k+39)n+5k^2+9k+86)/86400 TableForm[Table[u[n, k], {n, 1, 10}, {k, 1, 15}]] Table[u[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten CROSSREFS Cf. A000027, A185506, A185507, A185508. Cf. A000579 (column 1), A257200 (row 1). Sequence in context: A048062 A295729 A081284 * A099572 A288705 A287097 Adjacent sequences:  A185506 A185507 A185508 * A185510 A185511 A185512 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 29 2011 STATUS approved

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Last modified May 14 22:40 EDT 2021. Contains 343909 sequences. (Running on oeis4.)