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 A294035 a(n) = 3^n*hypergeom([-n/3, (1-n)/3, (2-n)/3], [1, 1], -1). 3
 1, 3, 9, 33, 153, 783, 4059, 21087, 110889, 592899, 3214989, 17608077, 97150491, 539331237, 3010588317, 16887545793, 95134584969, 537942476907, 3051902823849, 17365639042449, 99076018204413, 566622950463099, 3247670747106927, 18651711493531539, 107315246617831179 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Diagonal of rational function 1/(1 - (x^3 + y^3 + z^3 + 3*x*y*z)). - Gheorghe Coserea, Aug 04 2018 LINKS Robert Israel, Table of n, a(n) for n = 0..1288 FORMULA Let H(m, n, x) = m^n*hypergeom([(k-n)/m for k=0..m-1], [1 for k=0..m-2], x) then a(n) = H(3, n, -1). a(n) ~ sqrt(3) * 6^n / (Pi*n) . - Vaclav Kotesovec, Nov 02 2017 -(54*(n+2))*(n+1)*a(n)+27*(n+2)^2*a(n+1)-(3*(3*n^2+15*n+19))*a(n+2)+(n+3)^2*a(n+3) = 0. - Robert Israel, Nov 02 2017 MAPLE T := (m, n, x) -> m^n*hypergeom([seq((k-n)/m, k=0..m-1)], [seq(1, k=0..m-2)], x): seq(simplify(T(3, n, -1)), n=0..39); MATHEMATICA Table[3^n * HypergeometricPFQ[{-n/3, (1 - n)/3, (2 - n)/3}, {1, 1}, -1], {n, 0, 30}] (* Vaclav Kotesovec, Nov 02 2017 *) CROSSREFS H(1, n, 1) = A000007(n), H(2, n, 1) = A000984(n), H(3, n, 1) = A006077(n), H(4, n, 1) = A294036(n), H(1, n, -1) = A000079(n), H(2, n, -1) = A098335(n), H(3, n, -1) = this seq., H(4, n, -1) = A294037(n). Sequence in context: A180632 A279840 A009220 * A007489 A294638 A201968 Adjacent sequences:  A294032 A294033 A294034 * A294036 A294037 A294038 KEYWORD nonn AUTHOR Peter Luschny, Nov 02 2017 STATUS approved

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Last modified September 26 10:33 EDT 2020. Contains 337346 sequences. (Running on oeis4.)