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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.)