A394490 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + 5*x)^(3/5) ).

1, 3, 12, 42, 0, -1872, -12672, 172368, 4523904, 0, -1822818816, -27025270272, 717889277952, 33841118158848, 0, -36760473537435648, -836717934176796672, 32958199117834518528, 2237077674319512600576, 0, -4686406322165888889913344, -143728876497857181683023872

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))^(3/5).

a(n) = 5^n * n! * binomial(3*(n+1)/5,n)/(n+1).

a(5*n+4) = 0.

Mathematica

a[n_]:=5^n*n!*Binomial[3*( 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(3*(n+1)/5, n)/(n+1);
(Magma) [1] cat [5^n*Factorial(n)*&*[(3*(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, A394489, A394491.

Sequence in context: A038342 A260153 A328299 * A135264 A358690 A084529

Adjacent sequences: A394487 A394488 A394489 * A394491 A394492 A394493

Keyword

sign,easy

Author

Seiichi Manyama, Mar 22 2026

Status

approved