A394489 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + 5*x)^(2/5) ).

1, 2, 2, -12, 0, 672, -4752, -66528, 1782144, 0, -737807616, 11042583552, 295601467392, -14024247164928, 0, 15388105201717248, -351664059291697152, -13900737042896191488, 946455939135178407936, 0, -1993069355403883780767744, 61261488343348962684567552, 3203067102166891352025464832

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

E.g.f. A(x) satisfies A(x) = (1 + 5*x*A(x))^(2/5).

a(n) = 5^n * n! * binomial(2*(n+1)/5,n)/(n+1).

a(5*n+4) = 0.

Mathematica

a[n_]:=5^n*n!*Binomial[2*( n+1)/5, n]/(n+1); Table[a[n], {n, 0, 18}] (* Vincenzo Librandi, Mar 31 2026 *)

Prog

(PARI) a(n) = 5^n*n!*binomial(2*(n+1)/5, n)/(n+1);
(Magma) [1] cat [5^n*Factorial(n)*&*[ (2*(n+1)/5-k): k in [0..n-1]]/Factorial(n)/(n+1): n in [1..20] ]; // Vincenzo Librandi, Mar 31 2026

Crossrefs

Cf. A394488, A394490, A394491.

Sequence in context: A095215 A264712 A217094 * A392364 A076976 A291757

Adjacent sequences: A394486 A394487 A394488 * A394490 A394491 A394492

Keyword

sign,easy

Author

Seiichi Manyama, Mar 22 2026

Status

approved