A385207 G.f. A(x) satisfies A(x) = ( 1 + 49*x*A(x)^6 )^(1/7).

1, 7, 147, 3430, 79233, 1714314, 32471124, 450360372, 0, -313409171166, -15459345780879, -537166232508360, -15185812043764453, -348420909370148580, -5588125164812112720, 0, 4783756561471246040577, 254794190560328322173970, 9445124186699596552669050

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = 49^n * binomial(6*n/7+1/7,n)/(6*n+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^5).

G.f.: ( (1/x) * Series_Reversion(x/(1+49*x)^(6/7)) )^(1/6).

a(7*n+1) = 0 for n > 0.

G.f.: 1/B(-x), where B(x) is the g.f. of A385206.

Mathematica

a[n_] := 49^n * Binomial[6*n/7 + 1/7, n]/(6*n + 1); Array[a, 19, 0] (* Amiram Eldar, Nov 25 2025 *)

Prog

(PARI) a(n) = 49^n*binomial(6*n/7+1/7, n)/(6*n+1);

Crossrefs

Cf. A385206, A385208.

Cf. A182122, A376636, A385205.

Sequence in context: A211108 A382349 A251668 * A373881 A376227 A048935

Adjacent sequences: A385204 A385205 A385206 * A385208 A385209 A385210

Keyword

sign

Author

Seiichi Manyama, Jun 21 2025

Status

approved