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 A348893 a(n) = 840*(2*n)!/((n + 4)!*n!). 3
 35, 14, 14, 20, 35, 70, 154, 364, 910, 2380, 6460, 18088, 52003, 152950, 458850, 1400700, 4342170, 13646820, 43421700, 139704600, 454039950, 1489251036, 4925984196, 16419947320, 55124108860, 186281471320, 633357002488, 2165672331088, 7444498638115, 25717358931670, 89254363351090 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS FORMULA O.g.f: (140*z^3 - 70*z^2 + 14*z - 1 + (1 - 4*z)^(7/2))/(2*z^4). E.g.f: 64*exp(2*z)*((-z^3 - 1/2*z^2 - 1/4*z - 3/32)*BesselI(1,2*z) + BesselI(0,2*z)*z*(z^2 + 1/4*z + 3/32))/z^3. O.g.f g(z) satisfies z^4*g(z)^2 + (-140*z^3 + 70*z^2 - 14*z + 1)*g(z) + 4096*z^3 - 2268*z^2 + 476*z - 35 = 0; a(n) = Integral_{x=0..4} x^n*64*(1 - x/4)^(7/2)/(Pi*sqrt(x)). This is the integral representation as the n-th moment of a positive function on [0, 4]. The representation is unique. Remark: this sequence is not monotonically growing with n, as a(0) > a(1) = a(2)< a(3) < a(4)... . From Peter Luschny, Nov 03 2021: (Start) a(n) = 14*A007272(n)/(n + 4). a(n) ~ 105*4^n*(8*n - 81)/(n^(11/2)*sqrt(Pi)). a(n) = 4^(n + 4)*hypergeom([9/2, 1/2 - n], [11/2], 1) / (9*Pi). (End) a(n) = (-4)^(4 + n)*binomial(7/2, 4 + n)/2. - Peter Luschny, Nov 04 2021 MAPLE seq(840*(2*n)!/((n + 4)!*n!), n=0..30) MATHEMATICA a[n_] := 4^(n + 4) Hypergeometric2F1[9/2, 1/2 - n, 11/2, 1] / (9 Pi); Table[a[n], {n, 0, 30}] (* Peter Luschny, Nov 03 2021 *) PROG (Sage) def A348893(n): return (-4)^(4 + n)*binomial(7/2, 4 + n)/2 print([A348893(n) for n in range(31)])  # Peter Luschny, Nov 04 2021 CROSSREFS Row 3 of array A135573. Cf. A007054, A007272. Sequence in context: A051050 A267198 A267140 * A088830 A033355 A267402 Adjacent sequences:  A348885 A348886 A348887 * A348894 A348895 A348896 KEYWORD nonn,easy AUTHOR Karol A. Penson, Nov 02 2021 STATUS approved

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Last modified January 25 23:56 EST 2022. Contains 350572 sequences. (Running on oeis4.)