OFFSET
7,2
COMMENTS
If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for n>6, a(n) is equal to the number of (n+7)-subsets of X intersecting each X_i (i=1,2,...,n). - Milan Janjic, Jul 21 2007
LINKS
G. C. Greubel, Table of n, a(n) for n = 7..1000
Milan Janjic, Two Enumerative Functions.
Milan Janjic and Boris Petkovic, A Counting Function, arXiv:1301.4550 [math.CO], 2013.
Index entries for linear recurrences with constant coefficients, signature (16,-112,448,-1120,1792,-1792, 1024,-256).
FORMULA
a(n) = 2*a(n-1) + A002409(n-1).
a(n+8) = A082141(n+1)/2.
G.f.: x^7/(1-2*x)^8. - Colin Barker, Sep 04 2012
a(n) = Sum_{i=7..n} binomial(i,7)*binomial(n,i). Example: for n=11, a(11) = 1*330 + 8*165 + 36*55 + 120*11 + 330*1 = 5280. - Bruno Berselli, Mar 23 2018
From Amiram Eldar, Jan 06 2022: (Start)
Sum_{n>=7} 1/a(n) = 14*log(2) - 259/30.
Sum_{n>=7} (-1)^(n+1)/a(n) = 10206*log(3/2) - 124117/30. (End)
MAPLE
seq(binomial(n+7, 7)*2^n, n=0..21); # Zerinvary Lajos, Jun 23 2008
MATHEMATICA
Table[2^(n-7)*Binomial[n, 7], {n, 7, 30}] (* G. C. Greubel, Aug 27 2019 *)
PROG
(PARI) vector(23, n, 2^(n-1)*binomial(n+6, 7)) \\ G. C. Greubel, Aug 27 2019
(Magma) [2^(n-7)*Binomial(n, 7): n in [7..30]]; // G. C. Greubel, Aug 27 2019
(GAP) List([7..30], n-> 2^(n-7)*Binomial(n, 7)); # G. C. Greubel, Aug 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Apr 14 2000
EXTENSIONS
More terms from James A. Sellers, Apr 15 2000
STATUS
approved