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A394488

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

1, 1, -2, 6, 0, -504, 11232, -188496, 2306304, 0, -1359638784, 63494855424, -2024682283008, 43688279771136, 0, -67908377303230464, 4834297140281376768, -227335878221910441984, 7032746350114003943424, 0, -20948654383213967566700544, 2004699062001954538737893376

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OFFSET

0,3

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))^(1/5).

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

a(5*n+4) = 0.

MATHEMATICA

a[n_]:=5^n*n!*Binomial[( n+1)/5, n]/(n+1); Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, Apr 01 2026 *)

PROG