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URL: https://oeis.org/A394488

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A394488
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + 5*x)^(1/5) ).
6
1, 1, -2, 6, 0, -504, 11232, -188496, 2306304, 0, -1359638784, 63494855424, -2024682283008, 43688279771136, 0, -67908377303230464, 4834297140281376768, -227335878221910441984, 7032746350114003943424, 0, -20948654383213967566700544, 2004699062001954538737893376
OFFSET
0,3
LINKS
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
(PARI) a(n) = 5^n*n!*binomial((n+1)/5, n)/(n+1);
(Magma) [1] cat [5^n*Factorial(n)*&*[((n+1)/5-k): k in [0..n-1]]/Factorial(n)/(n+1): n in [1..20] ]; // Vincenzo Librandi, Apr 01 2026
KEYWORD
sign,easy,changed
AUTHOR
Seiichi Manyama, Mar 22 2026
STATUS
approved