OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (8,-21,35,-35,21,-7,1).
FORMULA
a(n) = A005709(7*n-3).
a(n) = Sum_{k=0..n} binomial(n+3+6*k,n-1-k).
a(n) = 8*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: x*(1-x)^2/((1-x)^7 - x).
a(n) = n*(1 + n)*(2 + n)*(3 + n)*hypergeom([1-n, (4+n)/6, (5+n)/6, 1+n/6, (7+n)/6, (8+n)/6, (9+n)/6], [5/7, 6/7, 8/7, 9/7, 10/7, 11/7], -6^6/7^7)/24. - Stefano Spezia, Jun 23 2024
MATHEMATICA
a[n_]:=n*(1 + n)*(2 + n)*(3 + n)*HypergeometricPFQ[{1-n, (4+n)/6, (5+n)/6, 1+n/6, (7+n)/6, (8+n)/6, (9+n)/6}, {5/7, 6/7, 8/7, 9/7, 10/7, 11/7}, -6^6/7^7]/24; Array[a, 24] (* Stefano Spezia, Jun 23 2024 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+3+6*k, n-1-k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 23 2024
STATUS
approved