The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A275457 G.f.: 3F2([2/9, 4/9, 5/9], [1/3, 1], 729 x). 1
 1, 120, 45045, 21707400, 11708971560, 6735720993408, 4039678502036100, 2494516661768577600, 1573990406710539567750, 1009797626141015909237040, 656436978973434195655059942, 431326871057383042747830748560, 285942228994752084893009228453460, 190985447073724962020463006948873600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS "Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link). LINKS Gheorghe Coserea, Table of n, a(n) for n = 0..300 A. Bostan, S. Boukraa, G. Christol, S. Hassani, J-M. Maillard Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity, arXiv:1211.6031 [math-ph], 2012. FORMULA G.f.: hypergeom([2/9, 4/9, 5/9], [1/3, 1], 729*x). From Robert Israel, Jan 20 2017: (Start) a(n) = (2/3)*729^n*Gamma(5/9+n)*Gamma(2/9+n)*Gamma(4/9+n)*sin((4/9)*Pi)*3^(1/2)/(Gamma(2/9)*Gamma(n+1)^2*Gamma(n+1/3)*Gamma(2/3)). a(n+1) = 3*(5+9*n)*(2+9*n)*(4+9*n)*a(n)/((n+1)^2*(3*n+1)). a(n) ~ (2*sin(4*Pi/9)/(sqrt(3)*Gamma(2/9)*Gamma(2/3))*729^n/n^(10/9). A007949(a(n)) = A053735(n). (End) EXAMPLE 1 + 120*x + 45045*x^2 + 21707400*x^3 + ... MAPLE A[0]:= 1: for n from 0 to 20 do A[n+1]:= 3*(5+9*n)*(2+9*n)*(4+9*n)*A[n]/((n+1)^2*(3*n+1)) od: seq(A[i], i=0..21); # Robert Israel, Jan 20 2017 MATHEMATICA CoefficientList[HypergeometricPFQ[{2/9, 4/9, 5/9}, {1/3, 1}, 729 x] + O[x]^14, x] (* Jean-François Alcover, Sep 18 2018 *) PROG (PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi"); read("hypergeom.gpi"); N = 12; x = 'x + O('x^N); Vec(hypergeom([2/9, 4/9, 5/9], [1/3, 1], 729*x, N)) CROSSREFS Cf. A007949, A053735, A268545-A268555, A275051-A275054. Sequence in context: A145407 A010798 A283829 * A265873 A146550 A006176 Adjacent sequences:  A275454 A275455 A275456 * A275458 A275459 A275460 KEYWORD nonn AUTHOR Gheorghe Coserea, Jul 31 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)