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 A110518 Riordan array (1, x*c(3x)), c(x) the g.f. of A000108. 6
 1, 0, 1, 0, 3, 1, 0, 18, 6, 1, 0, 135, 45, 9, 1, 0, 1134, 378, 81, 12, 1, 0, 10206, 3402, 756, 126, 15, 1, 0, 96228, 32076, 7290, 1296, 180, 18, 1, 0, 938223, 312741, 72171, 13365, 2025, 243, 21, 1, 0, 9382230, 3127410, 729729, 138996, 22275, 2970, 315, 24, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are C(3;n), A064063. Inverse is A110517. Diagonal sums are A110525. LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA Number triangle: T(0,k) = 0^k, T(n,k) = (k/n)*C(2n-k-1, n-k)*3^(n-k), n > 0, k > 0. T(n,k) = A106566(n,k)*3^(n-k). - Philippe Deléham, Nov 08 2007 Triangle T(n,k), 0 <= k <= n, read by rows, given by (0, 3, 3, 3, 3, 3, 3, 3, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Sep 23 2014 EXAMPLE Rows begin   1;   0,    1;   0,    3,    1;   0,   18,    6,    1;   0,  135,   45,    9,    1;   0, 1134,  378,   81,   12,    1;   ... Production matrix begins:   0,   1;   0,   3,   1;   0,   9,   3,   1;   0,  27,   9,   3,   1;   0,  81,  27,   9,   3,   1;   0, 243,  81,  27,   9,   3,   1;   ... - Philippe Deléham, Sep 23 2014 MATHEMATICA T[0, 0] := 1; T[0, k_] := 0; T[n_, k_] := (k/n)*3^(n - k)*Binomial[2*n - k - 1, n - k]; Table[T[n, k], {n, 0, 20}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 29 2017 *) PROG (PARI) concat([1], for(n=1, 10, for(k=0, n, print1((k/n)*3^(n-k)*binomial(2*n-k-1, n-k), ", ")))) \\ G. C. Greubel, Aug 29 2017 CROSSREFS Sequence in context: A243098 A241981 A147723 * A246049 A316773 A006837 Adjacent sequences:  A110515 A110516 A110517 * A110519 A110520 A110521 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Jul 24 2005 STATUS approved

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Last modified October 20 15:45 EDT 2019. Contains 328267 sequences. (Running on oeis4.)