OFFSET
0,2
REFERENCES
A. 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 (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = (9*n+8)*binomial(n+7, 7)/8.
G.f.: (1+8*x)/(1-x)^9.
From G. C. Greubel, Jan 18 2020: (Start)
a(n) = 9*binomial(n+8,8) - 8*binomial(n+7,7).
E.g.f.: (40320 + 645120*x + 1693440*x^2 + 1505280*x^3 + 588000*x^4 + 112896*x^5 + 10976*x^6 + 512*x^7 + 9*x^8)*exp(x)/40320. (End)
MAPLE
seq( (9*n+8)*binomial(n+7, 7)/8, n=0..30); # G. C. Greubel, Jan 18 2020
MATHEMATICA
Table[9*Binomial[n+8, 8] -8*Binomial[n+7, 7], {n, 0, 30}] (* G. C. Greubel, Jan 18 2020 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 17, 117, 525, 1815, 5247, 13299, 30459, 64350}, 30] (* Harvey P. Dale, Nov 23 2022 *)
PROG
(PARI) vector(31, n, (9*n-1)*binomial(n+6, 7)/8) \\ G. C. Greubel, Jan 18 2020
(Magma) [(9*n+8)*Binomial(n+7, 7)/8: n in [0..30]]; // G. C. Greubel, Jan 18 2020
(Sage) [(9*n+8)*binomial(n+7, 7)/8 for n in (0..30)] # G. C. Greubel, Jan 18 2020
(GAP) List([0..30], n-> (9*n+8)*Binomial(n+7, 7)/8 ); # G. C. Greubel, Jan 18 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jul 04 2000
STATUS
approved