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A346671
a(n) = Sum_{k=0..n} binomial(7*k,k) / (6*k + 1).
7
1, 2, 9, 79, 898, 11370, 153148, 2150836, 31140511, 461462144, 6964815000, 106691488130, 1654539334220, 25923944408960, 409770113121064, 6526344613981944, 104632592920840659, 1687270854882480906, 27348675382672733281, 445328790513987869681, 7281393330439106226281
OFFSET
0,2
COMMENTS
Partial sums of A002296.
LINKS
FORMULA
G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x * (1 - x)^6 * A(x)^7.
a(n) ~ 7^(7*n + 15/2) / (776887 * sqrt(Pi) * n^(3/2) * 2^(6*n + 2) * 3^(6*n + 3/2)). - Vaclav Kotesovec, Jul 30 2021
MATHEMATICA
Table[Sum[Binomial[7 k, k]/(6 k + 1), {k, 0, n}], {n, 0, 20}]
nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 - x) + x (1 - x)^6 A[x]^7 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
PROG
(PARI) a(n) = sum(k=0, n, binomial(7*k, k)/(6*k+1)); \\ Michel Marcus, Jul 28 2021
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 28 2021
STATUS
approved