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 A050165 Triangle read by rows: T(n,k)=M(2n+1,k,-1), 0<=k<=n, n >= 0, array M as in A050144. 3
 1, 1, 1, 1, 3, 2, 1, 5, 9, 5, 1, 7, 20, 28, 14, 1, 9, 35, 75, 90, 42, 1, 11, 54, 154, 275, 297, 132, 1, 13, 77, 273, 637, 1001, 1001, 429, 1, 15, 104, 440, 1260, 2548, 3640, 3432, 1430, 1, 17, 135, 663, 2244, 5508, 9996, 13260, 11934 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T is a mirror image of the array in A039599. LINKS M. W. Coffey, M. C. Lettington, On Fibonacci Polynomial Expressions for Sums of mth Powers, their implications for Faulhaber's Formula and some Theorems of Fermat, arXiv:1510.05402 [math.NT], 2015. See Section 4. FORMULA Triangle T(n, k) read by rows; given by [1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938. T(n, k) = C(2n, k)*(2n-2k+1)/(2n-k+1) . - Philippe Deléham, Dec 07 2003 Sum_{k=0 ..inf(m, n)} T(m, m-k)*T(n, n-k)= A000108(m+n); A000108: Catalan numbers. - Philippe Deléham, Dec 30 2003 T(n, k) = 0 if nk : T(n, k) = Sum_{j=0..k} T(n-1-j, k-j)*A000108(j+1) . - Philippe Deléham, Feb 03 2004 T(n,k)= Sum_{j, j>=0} (-1)^(n-j)*A094385(n,j)*binomial(j,k) . - Philippe Deléham, May 05 2007 T(2n,n) = A126596(n) . - From Philippe Deléham, Nov 23 2011 EXAMPLE Rows: {1}; {1,1}; {1,3,2}; ... Triangle begins : 1 1, 1 1, 3, 2 1, 5, 9, 5 1, 7, 20, 28, 14 1, 9, 35, 75, 90, 42 1, 11, 54, 154, 275, 297, 132 CROSSREFS Cf. A039599, A084938. Sequence in context: A021912 A114597 A199479 * A198876 A033878 A144061 Adjacent sequences:  A050162 A050163 A050164 * A050166 A050167 A050168 KEYWORD nonn,tabl AUTHOR STATUS approved

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Last modified October 16 13:32 EDT 2019. Contains 328093 sequences. (Running on oeis4.)