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 A123490 Triangle whose k-th column satisfies a(n) = (k+3)*a(n-1)-(k+2)*a(n-2). 3
 1, 2, 1, 4, 2, 1, 8, 5, 2, 1, 16, 14, 6, 2, 1, 32, 41, 22, 7, 2, 1, 64, 122, 86, 32, 8, 2, 1, 128, 365, 342, 157, 44, 9, 2, 1, 256, 1094, 1366, 782, 260, 58, 10, 2, 1, 512, 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1, 1024, 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA Column k has g.f.: x^k*(1-x(1+k))/((1-x)*(1-x(2+k))). T(n,k) = ((k+2)^(n-k)+k)/(k+1), for 0 <= k <= n. EXAMPLE Triangle begins 1, 2, 1, 4, 2, 1, 8, 5, 2, 1, 16, 14, 6, 2, 1, 32, 41, 22, 7, 2, 1, 64, 122, 86, 32, 8, 2, 1, 128, 365, 342, 157, 44, 9, 2, 1, 256, 1094, 1366, 782, 260, 58, 10, 2, 1, 512, 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1, 1024, 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1 MATHEMATICA Table[((k + 2)^(n - k) + k)/(k + 1), {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Oct 14 2017 *) PROG (PARI) for(n=0, 10, for(k=0, n, print1(((k+2)^(n-k)+k)/(k+1), ", "))) \\ G. C. Greubel, Oct 14 2017 CROSSREFS Columns include A000079, A007051, A047849, A047850, A047851. Row sums are A103439. Diagonal sums are A123491. Cf. A047848. Sequence in context: A228565 A054453 A109433 * A157028 A060637 A123486 Adjacent sequences:  A123487 A123488 A123489 * A123491 A123492 A123493 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Oct 01 2006 STATUS approved

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Last modified June 4 11:32 EDT 2020. Contains 334825 sequences. (Running on oeis4.)