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 A121682 Triangle read by rows: T(i,j) = (T(i-1,j) + i)*i. 2
 1, 6, 4, 27, 21, 9, 124, 100, 52, 16, 645, 525, 285, 105, 25, 3906, 3186, 1746, 666, 186, 36, 27391, 22351, 12271, 4711, 1351, 301, 49, 219192, 178872, 98232, 37752, 10872, 2472, 456, 64, 1972809, 1609929, 884169, 339849, 97929, 22329, 4185, 657, 81, 19728190, 16099390, 8841790, 3398590, 979390, 223390, 41950, 6670, 910, 100 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The first column is A030297 = a(n) = n*(n+a(n-1)). The main diagonal are the squares A000290 = n^2. The first lower diagonal (6,21,52,...) is A069778 = q-factorial numbers 3!_q. See also A121662. REFERENCES T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445. LINKS Table of n, a(n) for n=1..55. EXAMPLE Triangle begins: 1 6 4 27 21 9 124 100 52 16 645 525 285 105 25 3906 3186 1746 666 186 36 27391 22351 12271 4711 1351 301 49 ... MAPLE T:= proc(i, j) option remember; `if`(j<1 or j>i, 0, (T(i-1, j)+i)*i) end: seq(seq(T(n, k), k=1..n), n=1..10); # Alois P. Heinz, Jun 22 2022 MATHEMATICA T[n_, k_] /; 1 <= k <= n := T[n, k] = (T[n-1, k]+n)*n; T[_, _] = 0; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 17 2022 *) PROG (Python) def T(i, j): return (T(i-1, j)+i)*i if 1 <= j <= i else 0 print([T(r, c) for r in range(1, 11) for c in range(1, r+1)]) # Michael S. Branicky, Jun 22 2022 CROSSREFS Cf. A030297, A000290, A069778, A121662. Row sums give A337001. Sequence in context: A129886 A133837 A211945 * A237425 A191567 A274707 Adjacent sequences: A121679 A121680 A121681 * A121683 A121684 A121685 KEYWORD nonn,tabl AUTHOR Thomas Wieder, Aug 15 2006 EXTENSIONS Edited by N. J. A. Sloane, Sep 15 2006 Formula in name corrected by Alois P. Heinz, Jun 22 2022 STATUS approved

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Last modified May 23 05:11 EDT 2024. Contains 372758 sequences. (Running on oeis4.)