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A109345
a(n) = 5^((n^2 - n)/2).
10
1, 1, 5, 125, 15625, 9765625, 30517578125, 476837158203125, 37252902984619140625, 14551915228366851806640625, 28421709430404007434844970703125
OFFSET
0,3
COMMENTS
Sequence given by the Hankel transform (see A001906 for definition) of A078009 = {1, 1, 6, 41, 306, 2426, 20076, 171481, ...}; example: det([1, 1, 6, 41; 1, 6, 41, 306; 6, 41, 306, 2426; 41, 306, 2426, 20076]) = 5^6 = 15625.
a(n) is the number of simple labeled graphs, with bi-directional and non-directed edges allowed and not regarded as equivalent, on n labeled nodes. - Mark Stander, Feb 07 2019
LINKS
FORMULA
a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(5i, j).
G.f. A(x) satisfies: A(x) = 1 + x * A(5*x). - Ilya Gutkovskiy, Jun 04 2020
MAPLE
seq(5^(binomial(2+n, n)), n=-2..8); # Zerinvary Lajos, Jun 12 2007
MATHEMATICA
5^Binomial[Range[0, 12], 2] (* G. C. Greubel, Feb 09 2019 *)
PROG
(PARI) a(n)=5^binomial(n, 2) \\ Charles R Greathouse IV, Jan 11 2012
(Magma) [5^Binomial(n, 2): n in [0..12]]; // G. C. Greubel, Feb 09 2019
(Sage) [5^binomial(n, 2) for n in (0..12)] # G. C. Greubel, Feb 09 2019
(GAP) List([0..12], n -> 5^Binomial(n, 2)); # G. C. Greubel, Feb 09 2019
CROSSREFS
Cf. A006125 (number of graphs on n labeled nodes), A047656 (number of semi-complete digraphs on n labeled nodes), A053763 (number of simple digraphs on n labeled nodes), A053764.
Sequence in context: A013710 A202628 A358110 * A194502 A229868 A201839
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Aug 21 2005
STATUS
approved