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A394491
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + 5*x)^(4/5) ).
4
1, 4, 28, 264, 3000, 38304, 516672, 6785856, 71495424, 0, -35350608384, -1560159304704, -47580033650688, -990267674812416, 0, 1456943367596580864, 101520239945908912128, 4686616566420922957824, 142664283102312651423744, 0, -413735924068475859442335744, -39150593446155818050645917696
OFFSET
0,2
LINKS
FORMULA
E.g.f. A(x) satisfies A(x) = (1 + 5*x*A(x))^(4/5).
a(n) = 5^n * n! * binomial(4*(n+1)/5,n)/(n+1).
a(5*n+4) = 0 for n > 0.
MATHEMATICA
a[n_]:=5^n*n!*Binomial[4*( 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(4*(n+1)/5, n)/(n+1);
(Magma) [1] cat [5^n*Factorial(n)*&*[(4*(n+1)/5-k): k in [0..n-1]] / Factorial(n)/(n+1): n in [1..20] ]; // Vincenzo Librandi, Mar 31 2026
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Mar 22 2026
STATUS
approved