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A094213
a(n) = Sum_{k=0..n} binomial(9*n,9*k).
9
1, 2, 48622, 9373652, 9263421862, 3433541316152, 2140802758677844, 984101481334553024, 536617781178725122150, 265166261617029717011822, 138567978655457801631498052, 70126939586658252408697345838, 36144812798331420987905742371116
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (265,139823,-6826204,-6965249,512).
FORMULA
Let b(n) = a(n)-2^(9*n)/9 then b(n)+246*b(n-1)-13605*b(n-2)+b(n-3)+(-1)^n*3078=0.
Conjectures from Colin Barker, May 27 2019: (Start)
G.f.: (1 - 263*x - 91731*x^2 + 3035380*x^3 + 1547833*x^4) / ((1 + x)*(1 - 512*x)*(1 + 246*x - 13605*x^2 + x^3)).
a(n) = 265*a(n-1) + 139823*a(n-2) - 6826204*a(n-3) - 6965249*a(n-4) + 512*a(n-5) for n>4.
(End)
MATHEMATICA
Table[Sum[Binomial[9n, 9k], {k, 0, n}], {n, 0, 15}] (* Harvey P. Dale, Jul 14 2019 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(9*n, 9*k))
(PARI) Vec((1 - 263*x - 91731*x^2 + 3035380*x^3 + 1547833*x^4) / ((1 + x)*(1 - 512*x)*(1 + 246*x - 13605*x^2 + x^3)) + O(x^15)) \\ Colin Barker, May 27 2019
CROSSREFS
Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), A070782 (b=5), A070967 (b=6), A094211 (b=7), A070832 (b=8), this sequence (b=9), A070833 (b=10).
Sequence in context: A157959 A364134 A290047 * A321382 A153924 A059764
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, May 27 2004
STATUS
approved