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A109901
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a(n) = binomial(n^2, n*(n+1)/2).
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2
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1, 1, 4, 84, 8008, 3268760, 5567902560, 39049918716424, 1118770292985239888, 130276394656770614583240, 61448471214136179596720592960, 117118180539414377821494470432491764, 900390992257782351906806257139068209113040, 27883369051325994219981405855549095749234579210080
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OFFSET
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0,3
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COMMENTS
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8*a(2*n+1)^4 = A182010(n) = number of potential group developed cocyclic Hadamard matrices over (the group) Z_{(2*n+1)^2} X Z^2_2 [Baliga, et al., p. 130]. - L. Edson Jeffery, Apr 10 2012
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..50
A. Baliga and K. J. Horadam, Cocyclic Hadamard matrices over Z_t X Z^2_2, Australas. J. Combin. 11(1995), 123-134.
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FORMULA
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a(n) = C(n^2, n*(n+1)/2) = (n^2!)/((n(n+1)/2)!*(n(n-1)/2)!).
a(n) = C(n^2, n*(n-1)/2).
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EXAMPLE
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a(6) = 36!/(21!*15!) = 5567902560.
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MAPLE
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seq(binomial(n^2, n*(n+1)/2), n=0..12); # Emeric Deutsch, Jul 16 2005
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MATHEMATICA
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Table[Binomial[n^2, (n(n+1))/2], {n, 20}] (* Harvey P. Dale, Jun 04 2011 *)
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PROG
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(PARI) a(n)=binomial(n^2, n*(n+1)/2)
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CROSSREFS
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Cf. variants: A014062 (C(n^2,n*(n-1)), A135757 (C(n*(n+1),n*(n+1)/2)).
Cf. A182010.
Sequence in context: A012189 A012076 A173211 * A015018 A204245 A287248
Adjacent sequences: A109898 A109899 A109900 * A109902 A109903 A109904
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy, Jul 14 2005
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EXTENSIONS
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More terms from Emeric Deutsch, Jul 16 2005
Offset changed to 0 (with a(0)=1), and name changed slightly by Paul D. Hanna, Jun 24 2011
Terms a(12) and beyond from Andrew Howroyd, Nov 09 2019
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STATUS
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approved
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