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A345883 G.f. A(x) satisfies: A(x) = x / exp(3 * Sum_{k>=1} A(x^k) / k). 1
1, -3, 12, -64, 372, -2268, 14394, -94296, 632328, -4317846, 29925108, -209966748, 1488507931, -10645680858, 76717312932, -556528367791, 4060765734816, -29782931545368, 219444442931836, -1623585342758532, 12057148232386980, -89842712017158526, 671521130395037280 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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} 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), 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[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[d a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 23}]
CROSSREFS
Sequence in context: A276743 A203508 A052757 * A365122 A233397 A206226
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 28 2021
STATUS
approved

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Last modified April 12 09:51 EDT 2024. Contains 371627 sequences. (Running on oeis4.)