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 A190736 Diagonal sums of the Riordan matrix A121576. 1
 1, 2, 7, 29, 139, 731, 4096, 24005, 145420, 903503, 5726290, 36878978, 240663403, 1587928511, 10575884599, 71005972250, 480071241463, 3265685620913, 22335284505529, 153496543690226, 1059443187603955, 7340794592800628, 51042913856490028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA a(n) = [x^n](1-2*x-2*x^2)*(1+2*x)^(n+1)/((1+2*x-x^2+x^3)(1-x)^(n+1)). G.f.: (4-5*x-2*x^2-(2+x)*sqrt(1-8*x+4*x^2))/(2*(1-x+2*x^2+x^3)). Recurrence: 0 = 6*(n^2+17*n+72)*a(n+9) - (35*n^2+577*n+2376)*a(n+8) - (81*n^2+835*n+1856)*a(n+7) + (101*n^2+1017*n+2164)*a(n+6) - 2*(151*n^2+1883*n+5970)*a(n+5) - 2*(33*n^2+458*n+1528)*a(n+4) + (47*n^2+567*n+1564)*a(n+3) - 2*(7*n^2-16*n-120)*a(n+2) + 4*(3*n^2+8*n+4)*a(n+1) + 8*(n^2+3*n+2)*a(n). Conjecture: n*(11*n-35)*a(n) + 3*(-33*n^2+149*n-136)*a(n-1) +2*(77*n^2-377*n+396)*a(n-2) +(-209*n^2+1061*n-1200)*a(n-3) +12*(-11*n+30)*a(n-4) +4*(11*n-24)*(n-4)*a(n-5)=0. - R. J. Mathar, Jul 24 2012 MATHEMATICA CoefficientList[Series[(4-5x-2x^2-(2+x)Sqrt[1-8x+4x^2])/(2(1-x+2x^2 +x^3) ), {x, 0, 22}], x] PROG (PARI) x='x+O('x^30); Vec((4-5*x-2*x^2-(2+x)*sqrt(1-8*x+4*x^2))/(2*(1-x+2*x^2+x^3))) \\ G. C. Greubel, Apr 23 2018 (Magma) m:=25; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((4-5*x-2*x^2-(2+x)*Sqrt(1-8*x+4*x^2))/(2*(1-x+2*x^2+x^3)))); // G. C. Greubel, Apr 23 2018 CROSSREFS Cf. A121576. Sequence in context: A307389 A104252 A018977 * A265000 A347431 A355254 Adjacent sequences: A190733 A190734 A190735 * A190737 A190738 A190739 KEYWORD nonn AUTHOR Emanuele Munarini, May 18 2011 STATUS approved

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Last modified December 4 05:46 EST 2023. Contains 367541 sequences. (Running on oeis4.)