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 A289897 Number of matchings in the n-triangular honeycomb rook graph. 2
 1, 2, 8, 80, 2080, 158080, 36674560, 28019363840, 73410733260800, 697108323044556800, 24883978699398499532800, 3487539382678098506520985600, 1982680089210029713351206397542400, 4739557099654791829171791869197156352000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The n-triangular honeycomb rook graph is the disjoint union of the complete graphs K_k for k in {1..n}. In terms of a triangular chessboard it is the graph for a chesspiece that is constrained to move on a single axis. - Andrew Howroyd, Jul 17 2017 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..50 Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Matching FORMULA a(n) = Product_{k=1..n} A000085(k). - Andrew Howroyd, Jul 17 2017 MATHEMATICA FoldList[Times, Table[HypergeometricPFQ[{-k/2, (1 - k)/2}, {}, 2], {k, 20}]] (* Eric W. Weisstein, Jul 19 2017 *) Table[(-1/2)^(Binomial[n + 1, 2]/2) Product[HermiteH[k, -I/Sqrt[2]], {k, n}], {n, 20}] (* Eric W. Weisstein, Jul 19 2017 *) Table[Product[HypergeometricPFQ[{-k/2, (1 - k)/2}, {}, 2], {k, n}], {n, 20}] (* Eric W. Weisstein, Jul 19 2017 *) PROG (PARI) a(n) = prod(k=1, n, k! * polcoeff( exp( x + x^2 / 2 + x * O(x^k)), k)); \\ Andrew Howroyd, Jul 17 2017 CROSSREFS Cf. A289900. Sequence in context: A308088 A130530 A134529 * A134054 A323716 A229865 Adjacent sequences:  A289894 A289895 A289896 * A289898 A289899 A289900 KEYWORD nonn AUTHOR Eric W. Weisstein, Jul 14 2017 EXTENSIONS Terms a(11) and beyond from Andrew Howroyd, Jul 17 2017 STATUS approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)