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URL: https://oeis.org/A305724

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A305724
Crystal ball sequence for the lattice C_10.
2
1, 201, 7001, 104881, 927441, 5707449, 26986089, 104535009, 346615329, 1014889769, 2684641785, 6526963345, 14778775025, 31490462745, 63670078985, 122977987009, 228167048769, 408511495049, 708522994329, 1194315679089, 1962053519121, 3148993975161
OFFSET
0,2
COMMENTS
Partial sums of A035747.
LINKS
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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>10.
a(n) = Sum_{k=0..10} binomial(20, 2k)*binomial(n+k, 10).
G.f.: (1 + 6*x + x^2)*(1 + 184*x + 3740*x^2 + 16136*x^3 + 25414*x^4 + 16136*x^5 + 3740*x^6 + 184*x^7 + x^8) / (1 - x)^11. - Colin Barker, Jun 09 2018
PROG
(PARI) {a(n) = sum(k=0, 10, binomial(20, 2*k)*binomial(n+k, 10))}
(PARI) Vec((1 + 6*x + x^2)*(1 + 184*x + 3740*x^2 + 16136*x^3 + 25414*x^4 + 16136*x^5 + 3740*x^6 + 184*x^7 + x^8) / (1 - x)^11 + O(x^30)) \\ Colin Barker, Jun 09 2018
(GAP) b:=10;; List([0..25], n->Sum([0..b], k->Binomial(2*b, 2*k)*Binomial(n+k, b))); # Muniru A Asiru, Jun 09 2018
CROSSREFS
Sequence in context: A061697 A371109 A371057 * A167070 A175188 A227152
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 09 2018
STATUS
approved