OFFSET
0,2
COMMENTS
Partial sums of A052181.
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = (4*n+9)*binomial(n+8, 8)/9.
G.f.: (1+3*x)/(1-x)^10.
a(n) = 4*binomial(n+9,9) - 3*binomial(n+8,8). - G. C. Greubel, Jan 21 2020
Sum_{n>=0} 1/a(n) = 9437184*Pi/24035 + 56623104*log(2)/24035 - 482087736/168245. - Amiram Eldar, Feb 17 2023
MAPLE
seq( (4*n+9)*binomial(n+8, 8)/9, n=0..30); # G. C. Greubel, Jan 21 2020
MATHEMATICA
Table[4*Binomial[n+9, 9] - 3*Binomial[n+8, 8], {n, 0, 30}] (* G. C. Greubel, Jan 21 2020 *)
PROG
(PARI) vector(31, n, (4*n+5)*binomial(n+7, 8)/9) \\ G. C. Greubel, Jan 21 2020
(Magma) [(4*n+9)*Binomial(n+8, 8)/9: n in [0..30]]; // G. C. Greubel, Jan 21 2020
(Sage) [(4*n+9)*binomial(n+8, 8)/9 for n in (0..30)] # G. C. Greubel, Jan 21 2020
(GAP) List([0..30], n-> (4*n+9)*Binomial(n+8, 8)/9 ); # G. C. Greubel, Jan 21 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, May 30 2000
STATUS
approved