A186231 Expansion of ( 2F1([-1/4, 1/4]; [-1/2], 16*x) - 1 ) / (2*x).

1, 15, 210, 3003, 43758, 646646, 9657700, 145422675, 2203961430, 33578000610, 513791607420, 7890371113950, 121548660036300, 1877405874732108, 29065024282889672, 450883717216034179, 7007092303604022630, 109069992321755544170, 1700179760011004467468, 26536589497469056215210, 414670662257153823494820

Offset

0,2

Comments

Combinatorial interpretation welcome.

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

Number of North-East lattice paths from (0,0) to (n,n+1). - Michael D. Weiner, Apr 14 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = A001791(2n+1). - R. J. Mathar, Jul 10 2012

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

a(n) ~ 2^(4*n+3/2) / sqrt(Pi*n). - Amiram Eldar, Oct 03 2025

Mathematica

CoefficientList[Series[(HypergeometricPFQ[{-(1/4), 1/4}, {-(1/2)}, 16 x] - 1)/(2 x), {x, 0, 20}], x]
a[n_] := Binomial[4*n+2, 2*n]; Array[a, 30, 0] (* Amiram Eldar, Oct 03 2025 *)

Crossrefs

Cf. A000888, A001791, A135404, A186229.

Sequence in context: A170648 A170696 A170734 * A001880 A240682 A113362

Adjacent sequences: A186228 A186229 A186230 * A186232 A186233 A186234

Keyword

nonn,easy

Author

Olivier Gérard, Feb 15 2011

Status

approved