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A349334
G.f. A(x) satisfies A(x) = 1 + x * A(x)^7 / (1 - x).
8
1, 1, 8, 85, 1051, 14197, 203064, 3022909, 46347534, 726894786, 11606936525, 188060979332, 3084087347910, 51094209834068, 853859480938095, 14376597494941454, 243649099741045190, 4153091242153905838, 71152973167920086796, 1224593757045581062444
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} binomial(n-1,k-1) * binomial(7*k,k) / (6*k+1).
a(n) ~ 870199^(n + 1/2) / (343 * sqrt(Pi) * n^(3/2) * 2^(6*n + 2) * 3^(6*n + 3/2)). - Vaclav Kotesovec, Nov 15 2021
MAPLE
a:= n-> coeff(series(RootOf(1+x*A^7/(1-x)-A, A), x, n+1), x, n):
seq(a(n), n=0..20); # Alois P. Heinz, Nov 15 2021
MATHEMATICA
nmax = 19; A[_] = 0; Do[A[x_] = 1 + x A[x]^7/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Sum[Binomial[n - 1, k - 1] Binomial[7 k, k]/(6 k + 1), {k, 0, n}], {n, 0, 19}]
PROG
(PARI) {a(n) = my(A=[1]); for(m=1, n, A=concat(A, 0);
A[#A] = 1 + sum(k=1, m-1, (polcoeff(Ser(A)^7, k)) )); A[n+1]}
for(n=0, 30, print1(a(n), ", ")) \\ Vaclav Kotesovec, Nov 23 2024, after Paul D. Hanna
CROSSREFS
Cf. A002296, A346649 (partial sums), A349363.
Sequence in context: A288691 A300675 A241323 * A261501 A371897 A180582
KEYWORD
nonn,changed
AUTHOR
Ilya Gutkovskiy, Nov 15 2021
STATUS
approved