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A331403
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E.g.f.: 1 / ((1 + x) * sqrt(1 - 2*x)).
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0
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1, 0, 3, 6, 81, 540, 7155, 85050, 1346625, 22339800, 431331075, 9004668750, 208178118225, 5199538043700, 140664514065075, 4080315642653250, 126613733680058625, 4180226398201854000, 146399020309066399875, 5419213146765629961750, 211446723837565171580625
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..20.
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FORMULA
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a(n) = n! * Sum_{k=0..n} (-1)^(n - k) * (2*k - 1)!! / k!.
D-finite with recurrence: a(n) +(-n+1)*a(n-1) -(2*n-1)*(n-1)*a(n-2)=0. - R. J. Mathar, Jan 25 2020
a(n) ~ 2^(n + 3/2) * n^n / (3*exp(n)). - Vaclav Kotesovec, Jan 26 2020
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MATHEMATICA
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nmax = 20; CoefficientList[Series[1/((1 + x) Sqrt[1 - 2 x]), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-1)^(n - k) (2 k - 1)!!/k!, {k, 0, n}], {n, 0, 20}]
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PROG
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(PARI) a(n) = {n! * sum(k=0, n, (-1)^(n - k) * (2*k)! / (2^k*k!^2))} \\ Andrew Howroyd, Jan 16 2020
(PARI) seq(n) = {Vec(serlaplace(1 / ((1 + x) * sqrt(1 - 2*x + O(x*x^n)))))} \\ Andrew Howroyd, Jan 16 2020
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CROSSREFS
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Cf. A001147, A005359, A034430, A052585, A317618.
Sequence in context: A350992 A213138 A349875 * A157197 A211896 A299433
Adjacent sequences: A331400 A331401 A331402 * A331404 A331405 A331406
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jan 16 2020
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STATUS
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approved
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