A380465 G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^2 )^(1/5).

1, 5, 125, 4250, 166250, 7052500, 315459375, 14648437500, 699404062500, 34120414453125, 1693355782421875, 85222795492187500, 4339218139648437500, 223115431527734375000, 11568972340119140625000, 604249120575386718750000, 31761084429202554931640625, 1678825356066226959228515625

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^7 )^(1/5).

a(n) = 25^n * binomial(7*n/5+1/5,n)/(7*n+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^9).

G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(7/5)) )^(1/7).

a(n) ~ 7^((14*n-3)/10) * 5^n / (2^(2*(n+3)/5) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Nov 25 2025

Mathematica

a[n_] := 25^n * Binomial[7*n/5 + 1/5, n]/(7*n + 1); Array[a, 18, 0] (* Amiram Eldar, Nov 25 2025 *)

Prog

(PARI) a(n) = 25^n*binomial(7*n/5+1/5, n)/(7*n+1);

Crossrefs

Cf. A034688, A078534, A385203, A385204, A385205, A380466, A380471.

Sequence in context: A195801 A154022 A013710 * A202628 A358110 A109345

Adjacent sequences: A380462 A380463 A380464 * A380466 A380467 A380468

Keyword

nonn

Author

Seiichi Manyama, Jun 23 2025

Status

approved