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
G. C. Greubel, Table of n, a(n) for n = 0..50
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
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Aug 21 2005
STATUS
approved