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URL: https://oeis.org/A345885

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A345885
G.f. A(x) satisfies: A(x) = x * exp(3 * Sum_{k>=1} (-1)^k * A(x^k) / k).
1
1, -3, 15, -82, 486, -3090, 20497, -140010, 979131, -6976603, 50461716, -369533691, 2734423934, -20414010219, 153571115619, -1163003999342, 8859172575069, -67835214598017, 521824159637718, -4030828937892966, 31252886542570119, -243142210911325273, 1897466281615297698
OFFSET
1,2
FORMULA
G.f.: x / Product_{n>=1} (1 + x^n)^(3*a(n)).
a(n+1) = (3/n) * Sum_{k=1..n} ( Sum_{d|k} (-1)^(k/d) * d * a(d) ) * a(n-k+1).
MAPLE
a:= proc(n) option remember; `if`(n=1, 1, 3*add(a(n-k)*add(d*a(d)
*(-1)^(k/d), d=numtheory[divisors](k)), k=1..n-1)/(n-1))
end:
seq(a(n), n=1..23); # Alois P. Heinz, Jun 28 2021
MATHEMATICA
nmax = 23; A[_] = 0; Do[A[x_] = x Exp[3 Sum[(-1)^k A[x^k]/k, {k, 1, nmax}]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = 1; a[n_] := a[n] = (3/(n - 1)) Sum[Sum[(-1)^(k/d) d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 28 2021
STATUS
approved