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A278596
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a(n) = Sum_{k=0..n} binomial(k+n+3,k)*binomial(2*n+1,n-k).
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1
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1, 8, 61, 462, 3504, 26664, 203632, 1560416, 11994112, 92445184, 714258944, 5530504192, 42905149440, 333427783680, 2595170856960, 20227227279360, 157854186209280, 1233319675822080, 9646098160680960, 75517231288811520
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (sqrt(1-8*x)+3)^2/(2*(sqrt(1-8*x)+1)^3*sqrt(1-8*x)).
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MATHEMATICA
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CoefficientList[Series[(Sqrt[1 - 8*x] + 3)^2/(2*(Sqrt[1 - 8*x] + 1)^3* Sqrt[1 - 8*x]), {x, 0, 50}], x] (* G. C. Greubel, Apr 09 2017 *)
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PROG
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(Maxima)
taylor((sqrt(1-8*x)+3)^2/(2*(sqrt(1-8*x)+1)^3*sqrt(1-8*x)), x, 0, 10);
(PARI) x='x+O('x^50); Vec((sqrt(1-8*x)+3)^2/(2*(sqrt(1-8*x) +1)^3*sqrt(1 -8*x))) \\ G. C. Greubel, Apr 09 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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