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 A206294 Riordan array (1, x/(1-x)^3). 1
 1, 0, 1, 0, 3, 1, 0, 6, 6, 1, 0, 10, 21, 9, 1, 0, 15, 56, 45, 12, 1, 0, 21, 126, 165, 78, 15, 1, 0, 28, 252, 495, 364, 120, 18, 1, 0, 36, 462, 1287, 1365, 680, 171, 21, 1, 0, 45, 792, 3003, 4368, 3060, 1140, 231, 24, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Triangle T(n,k), read by rows, given by (0, 3, -1, 2/3, -1/6, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. Row sums are A052529(n). LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n,0) = 0^n, T(n,k) = C(n-1+2k, n-k) for k > 0. T(n,n) = 1, T(k+1,k) = 3*k = A008585(k), T(k+2,k) = A081266(k). Sum_{k=0..n} T(n,k)*x^k = A000007(n), A052529(n), A052910(n) for x = 0, 1, 2 respectively. G.f.: (1-x)^3/((1-x)^3-y*x). EXAMPLE Triangle begins: 1 0, 1 0, 3, 1 0, 6, 6, 1 0, 10, 21, 9, 1 0, 15, 56, 45, 12, 1 0, 21, 126, 165, 78, 15, 1 0, 28, 252, 495, 364, 120, 18, 1 0, 36, 462, 1287, 1365, 680, 171, 21, 1 0, 45, 792, 3003, 4368, 3060, 1140, 231, 24, 1 0, 55, 1287, 6435, 12376, 11628, 5985, 1771, 300, 27, 1 0, 66, 2002, 12870, 31824, 38760, 26324, 10626, 2600, 378, 30, 1 MATHEMATICA Table[If[n == 0 && k == 0 , 1, Binomial[n - 1 + 2 k, n - k]], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 25 2017 *) PROG (PARI) {T(n, k)=polcoeff(1/(1-x+x*O(x^(n-k)))^(3*k), n-k)} (PARI) {T(n, k)=polcoeff(polcoeff((1-x)^3/((1-x)^3-y*x +x*O(x^n)), n, x), k, y)} for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print("")) CROSSREFS Cf. Columns: A000007, A000217 (triangular numbers), A000389, A000581, A001288, A010967..(+3)..A011000, A017714..(+3)..A017762. Cf. A127893. Sequence in context: A213668 A256595 A004590 * A058150 A058151 A257673 Adjacent sequences:  A206291 A206292 A206293 * A206295 A206296 A206297 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Feb 05 2012 STATUS approved

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Last modified October 15 11:59 EDT 2018. Contains 316231 sequences. (Running on oeis4.)