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Expansion of ( 2F1([-1/4, 1/4]; [-1/2], 16*x) - 1 ) / (2*x).
2

%I #24 Jul 27 2022 06:20:41

%S 1,15,210,3003,43758,646646,9657700,145422675,2203961430,33578000610,

%T 513791607420,7890371113950,121548660036300,1877405874732108,

%U 29065024282889672,450883717216034179,7007092303604022630,109069992321755544170,1700179760011004467468,26536589497469056215210,414670662257153823494820

%N Expansion of ( 2F1([-1/4, 1/4]; [-1/2], 16*x) - 1 ) / (2*x).

%C Combinatorial interpretation welcome.

%C Probably a class of paths (Cf. A135404, A000888).

%C Number of North-East lattice paths from (0,0) to (n,n+1). - _Michael D. Weiner_, Apr 14 2017

%H Vincenzo Librandi, <a href="/A186231/b186231.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = A001791(2n+1). - _R. J. Mathar_, Jul 10 2012

%F D-finite with recurrence -(n+1)*(2*n-1)*a(n) +2*(4*n-1)*(4*n+1)*a(n-1)=0. - _R. J. Mathar_, Apr 26 2017

%t CoefficientList[Series[(HypergeometricPFQ[{-(1/4), 1/4}, {-(1/2)}, 16 x] - 1)/(2 x), {x, 0, 20}], x]

%Y Cf. A186229.

%K nonn

%O 0,2

%A _Olivier GĂ©rard_, Feb 15 2011