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A372956
G.f. A(x) satisfies A(x)^5 = A(x^5) / (1 - 5*x)^5 with A(0)=1.
3
1, 5, 25, 125, 625, 3126, 15630, 78150, 390750, 1953750, 9768753, 48843765, 244218825, 1221094125, 6105470625, 30527353136, 152636765680, 763183828400, 3815919142000, 19079595710000, 95397978550044, 476989892750220, 2384949463751100, 11924747318755500, 59623736593777500
OFFSET
0,2
COMMENTS
Euler transform of 5 * A054662(n).
LINKS
FORMULA
G.f.: A(x) = 1 / ( Product_{k>=1} (1 - x^k)^A054662(k) )^5.
EXAMPLE
A(x)^5 = 1 + 25*x + 375*x^2 + 4375*x^3 + 43750*x^4 + 393755*x^5 + ... .
PROG
(PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
my(N=30, x='x+O('x^N)); Vec(1/prod(k=1, N, (1 - x^k)^b(k, 5))^5)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 04 2024
STATUS
approved