OFFSET
0,2
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = (n+1)*C(n+7, 7).
G.f.: (1+7*x)/(1-x)^9.
E.g.f.: (5040 +75600*x +194040*x^2 +170520*x^3 +66150*x^4 +12642*x^5 + 1225*x^6 +57*x^7 +x^8)*exp(x)/5040. - G. C. Greubel, Aug 29 2019
From Amiram Eldar, Jan 15 2023: (Start)
Sum_{n>=0} 1/a(n) = 7*Pi^2/6 - 37583/3600.
Sum_{n>=0} (-1)^n/a(n) = 7*Pi^2/12 - 2912*log(2)/15 + 155701/1200. (End)
MAPLE
seq((n+1)*binomial(n+7, 7), n=0..30); # G. C. Greubel, Aug 29 2019
MATHEMATICA
Table[(n+1)Binomial[n+7, 7], {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011; corrected by Bruno Berselli, Jan 23 2015 *)
PROG
(Haskell)
a056001 n = (n + 1) * a007318' (n + 7) 7
-- Reinhard Zumkeller, Aug 31 2014
(PARI) vector(30, n, n*binomial(n+6, 7)) \\ G. C. Greubel, Aug 29 2019
(Magma) [(n+1)*Binomial(n+7, 7): n in [0..30]]; // G. C. Greubel, Aug 29 2019
(Sage) [(n+1)*binomial(n+7, 7) for n in (0..30)] # G. C. Greubel, Aug 29 2019
(GAP) List([0..30], n-> (n+1)*Binomial(n+7, 7)); # G. C. Greubel, Aug 29 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, Jun 18 2000
STATUS
approved