A359647
a(n) = [x^n] hypergeom([1/4, 3/4], [2], 64*x). The central terms of the Motzkin triangle A359364 without zeros.
Original entry on oeis.org
1, 6, 140, 4620, 180180, 7759752, 356948592, 17210021400, 859544957700, 44123307828600, 2315270298060720, 123691561681243920, 6707888537328997200, 368417878127146461600, 20455964090297751153600, 1146556787261188952159280, 64797319609481605046295780
Offset: 0
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ser := series(hypergeom([1/4, 3/4], [2], 64*x), x, 20):
seq(coeff(ser, x, n), n = 0..16);
A025179
a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is an integer, s(0) = 0, |s(1)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2, s(n) = 1. Also a(n) = T(n,n-1), where T is the array defined in A025177.
Original entry on oeis.org
1, 4, 10, 29, 81, 231, 659, 1891, 5443, 15718, 45508, 132067, 384047, 1118820, 3264642, 9539787, 27913083, 81769236, 239794422, 703906719, 2068153899, 6081507831, 17896695831, 52703944965, 155310270101, 457956633826, 1351132539604
Offset: 2
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Rest[Rest[CoefficientList[Series[((1-x)^2-(1-x)*Sqrt[1-2*x-3*x^2]) /(2*x*Sqrt[1-2*x-3*x^2]), {x, 0, 20}], x]]] (* Vaclav Kotesovec, Feb 13 2014 *)
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my(x='x+O('x^50)); Vec(((1-x)^2-(1-x +2*x^2)*sqrt(1-2*x-3*x^2)) /(2*x*sqrt(1 - 2*x -3*x^2))) \\ G. C. Greubel, Mar 01 2017
A359649
a(n) = hypergeom([(1 - n)/2, -n/2], [2], 4*n^2).
Original entry on oeis.org
1, 1, 5, 28, 609, 6501, 272701, 4286815, 272156417, 5648748355, 484054204501, 12482361156398, 1351553781736225, 41650209565275195, 5460281206077347469, 195722005810272604876, 30156361094764202326017, 1232550298298392183231275, 218366864894707599746619685
Offset: 0
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a := n -> hypergeom([(1 - n)/2, -n/2], [2], 4*n^2):
seq(simplify(a(n)), n = 0..18);
Showing 1-3 of 3 results.
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