OFFSET
0,2
COMMENTS
Partial sums of A019564.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, Annales de l'institut Fourier, Tome 49 (1999) no. 3 , p. 727-762.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9), for n>8.
a(n) = Sum_{k=0..8} binomial(16, 2k)*binomial(n+k, 8).
G.f.: (1 + 120*x + 1820*x^2 + 8008*x^3 + 12870*x^4 + 8008*x^5 + 1820*x^6 + 120*x^7 + x^8) / (1 - x)^9. - Colin Barker, Jun 09 2018
PROG
(PARI) {a(n) = sum(k=0, 8, binomial(16, 2*k)*binomial(n+k, 8))}
(PARI) Vec((1 + 120*x + 1820*x^2 + 8008*x^3 + 12870*x^4 + 8008*x^5 + 1820*x^6 + 120*x^7 + x^8) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Jun 09 2018
(GAP) b:=8;; List([0..25], n->Sum([0..b], k->Binomial(2*b, 2*k)*Binomial(n+k, b))); # Muniru A Asiru, Jun 09 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 09 2018
STATUS
approved