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%I A145562 #14 May 26 2017 02:40:40
%S A145562 1,15,255,5175,123795,3427515,108046575,3824996175,150346471275,
%T A145562 6499426608675,306553491419175,15668768604864375,862827112324051875,
%U A145562 50929793720847916875,3208139019437586609375,214817175616326677769375,15237402314816854944646875
%N A145562 Second column (m=2) of triangle A049029 (S2(5)).
%H A145562 G. C. Greubel, <a href="/A145562/b145562.txt">Table of n, a(n) for n = 0..360</a>
%F A145562 a(n) = A049029(n+2,2),n>=0.
%F A145562 E.g.f. with offset n=2: ((-1+(1-4*x)^(-1/4))^2)/2!.
%F A145562 E.g.f.: (6 - 5*(1-4*x)^(1/4))/(1-4*x)^(5/2) (offset n=0).
%F A145562 a(n) = (-4)^n*(8*Sqrt(Pi)/Gamma(-3/2-n)-5*Gamma(-5/4)/Gamma(-5/4-n)). - _Benedict W. J. Irwin_, Apr 06 2017
%t A145562 FullSimplify@Table[(-4)^n(8Sqrt[Pi]/Gamma[-3/2-n]-5Gamma[-5/4]/Gamma[-5/4-n]),{n, 0, 20}] (* _Benedict W. J. Irwin_, Apr 06 2017 *)
%o A145562 (PARI) x='x+O('x^50); Vec(serlaplace((6 - 5*(1-4*x)^(1/4))/(1 -4*x)^(5/2))) \\ _G. C. Greubel_, May 25 2017
%Y A145562 First column: A007696 (4-factorials). Third column A143169.
%K A145562 nonn,easy
%O A145562 0,2
%A A145562 _Wolfdieter Lang_, Oct 17 2008, Dec 04 2008

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