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 A122897 Riordan array (1/(1-x), c(x)-1) where c(x) is the g.f. of A000108. 2
 1, 1, 1, 1, 3, 1, 1, 8, 5, 1, 1, 22, 19, 7, 1, 1, 64, 67, 34, 9, 1, 1, 196, 232, 144, 53, 11, 1, 1, 625, 804, 573, 261, 76, 13, 1, 1, 2055, 2806, 2211, 1171, 426, 103, 15, 1, 1, 6917, 9878, 8399 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Product of A007318 and A122896. Inverse of Riordan array ((1+x+x^2)/(1+x)^2,x/(1+x)^2). Row sums are A024718. The n-th row polynomial (in descending powers of x) equals the n-th Taylor polynomial of the rational function (1 - x^2)/(1 + x + x^2) * (1 + x)^(2*n) about 0. For example, for n = 4 we have (1 - x^2)/( 1 + x + x^2) * (1 + x)^8 = (x^4 + 22*x^3 +  19*x^2 + 7*x + 1) + O(x^5). - Peter Bala, Feb 21 2018 LINKS FORMULA T(n,k) =  binomial(2*n,n-k) + 2*Sum_{j = 1..n-k} cos((2/3)*Pi*j)* binomial(2*n, n-k-j). - Peter Bala, Feb 21 2018 EXAMPLE Triangle begins   1,   1,     1,   1,     3,     1,   1,     8,     5,     1,   1,    22,    19,     7,     1,   1,    64,    67,    34,     9,    1,   1,   196,   232,   144,    53,   11,    1,   1,   625,   804,   573,   261,   76,   13,   1,   1,  2055,  2806,  2211,  1171,  426,  103,  15,   1,   1,  6917,  9878,  8399,  4979, 2126,  647, 134,  17,  1,   1, 23713, 35072, 31655, 20483, 9878, 3554, 932, 169, 19, 1 MAPLE A122897 := proc (n, k)   binomial(2*n, n-k) + 2*add(cos((2/3)*Pi*j)*binomial(2*n, n-k-j), j = 1..n-k) end proc: for n from 0 to 10 do seq(A122897(n, k), k = 0..n) end do; # Peter Bala, Feb 21 2018 CROSSREFS Sequence in context: A114276 A152879 A098747 * A117425 A287215 A168216 Adjacent sequences:  A122894 A122895 A122896 * A122898 A122899 A122900 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Sep 18 2006 STATUS approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)