OFFSET
1,2
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
FORMULA
a(n) = n*(n-1)*(2*n+1)*(2*n-1)*(2*n-3)*(10*n+7)/90.
If we replace n with n-1/2 in this formula we get 16*A000586(n).
G.f.: z*(9+196*z+350*z**2+84*z**3+z**4)/(1-z)^7.
a(1)=0, a(2)=9, a(3)=259, a(4)=1974, a(5)=8778, a(6)=28743, a(7)=77077, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - Harvey P. Dale, Jun 09 2013
MAPLE
A001823:=-(9+196*z+350*z**2+84*z**3+z**4)/(z-1)**7; # conjectured (correctly) by Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[1/90*n*(n - 1)*(2*n + 1)*(2*n - 1)*(2*n - 3)*(10*n + 7), {n, 40}] (* Stefan Steinerberger, Apr 15 2006 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 9, 259, 1974, 8778, 28743, 77077}, 30] (* Harvey P. Dale, Jun 09 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Stefan Steinerberger, Apr 15 2006
STATUS
approved