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 A123162 Triangle read by rows: T(n,k) = binomial(2*n - 1, 2*k - 1) for 0 < k <= n and T(n,0) = 1. 3
 1, 1, 1, 1, 3, 1, 1, 5, 10, 1, 1, 7, 35, 21, 1, 1, 9, 84, 126, 36, 1, 1, 11, 165, 462, 330, 55, 1, 1, 13, 286, 1287, 1716, 715, 78, 1, 1, 15, 455, 3003, 6435, 5005, 1365, 105, 1, 1, 17, 680, 6188, 19448, 24310, 12376, 2380, 136, 1, 1, 19, 969, 11628, 50388 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Muniru A Asiru, Table of n, a(n) for n = 0..1325(rows 0 t0 50, flattened) FORMULA From Paul Barry, May 26 2008: (Start) T(n,k) = C(2n - 1, 2k - 1) + 0^k. Column k has g.f. (x^k/(1 - x)^(2*k + 0^k))*sum{j=0..k} C(2*k, 2*j)*x^j. (End) From Franck Maminirina Ramaharo, Oct 10 2018: (Start) Row n = coefficients in the expansion of ((x + sqrt(x))*(sqrt(x) - 1)^(2*n) + (x - sqrt(x))*(sqrt(x) + 1)^(2*n) + 2*x - 2)/(2*x - 2). G.f.: (1 - (2 + x)*y + (1 - 2*x)*y^2 - (x - x^2)*y^3)/(1 - (3 + 2*x)*y + (3 + x^2)*y^2 - (1 - 2*x + x^2)*y^3). E.g.f.: ((x + sqrt(x))*exp(y*(sqrt(x) - 1)^2) + (x - sqrt(x))*exp(y*(sqrt(x) + 1)^2) + (2*x - 2)*exp(y) - 2*x)/(2*x - 2). (End) EXAMPLE Triangle begins:      1;      1,  1;      1,  3,   1;      1,  5,  10,    1;      1,  7,  35,   21,    1;      1,  9,  84,  126,   36,    1;      1, 11, 165,  462,  330,   55,    1;      1, 13, 286, 1287, 1716,  715,   78,  1;      1, 15, 455, 3003, 6435, 5005, 1365, 105, 1;      ... MATHEMATICA T[n_, m_] = If [m == 0, 1, (2*n - 1)!/((2*(n - m))!*(2*m - 1)!)]; a = Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a] PROG (Maxima) T(n, k) := if k = 0 then 1 else binomial(2*n - 1, 2*k - 1)\$ tabl(nn) := for n:0 thru nn do print(makelist(T(n, k), k, 0, n))\$ /* Franck Maminirina Ramaharo, Oct 10 2018 */ (GAP) Flat(Concatenation([1], List([1..10], n->Concatenation([1], List([1..n], m->Binomial(2*n-1, 2*m-1)))))); # Muniru A Asiru, Oct 11 2018 CROSSREFS Cf. A007318, A034867, A103327, A122366. Sequence in context: A201588 A086385 A295222 * A213998 A294946 A083075 Adjacent sequences:  A123159 A123160 A123161 * A123163 A123164 A123165 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Oct 02 2006 EXTENSIONS Edited by N. J. A. Sloane, Oct 04 2006 Partially edited and offset corrected by Franck Maminirina Ramaharo, Oct 10 2018 STATUS approved

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Last modified November 21 03:20 EST 2018. Contains 317427 sequences. (Running on oeis4.)