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A305881 Expansion of Product_{k>=1} 1/(1 + prime(k)*x^k). 2
1, -2, 1, -7, 16, -28, 62, -118, 303, -630, 1152, -2426, 5315, -10718, 20482, -43449, 91111, -179254, 358910, -727829, 1484601, -2995681, 5924606, -11935441, 24382120, -48702245, 96682698, -195063604, 392983826, -784903199, 1569490057, -3146479152, 6317124649, -12652202092 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution inverse of A147655.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..3321

FORMULA

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*prime(j)^k*x^(j*k)/k).

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      b(n, i-1) +`if`(i>n, 0, b(n-i, i-1)*ithprime(i))))

    end:

a:= proc(n) option remember; `if`(n=0, 1,

      -add(b(n-i$2)*a(i$2), i=0..n-1))

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Jun 13 2018

MATHEMATICA

nmax = 33; CoefficientList[Series[Product[1/(1 + Prime[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 33; CoefficientList[Series[Exp[Sum[Sum[(-1)^k Prime[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (-Prime[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 33}]

CROSSREFS

Cf. A000040, A002099, A061151, A145519, A147655, A298160, A304791, A305882.

Sequence in context: A260259 A141488 A113042 * A184346 A178622 A013070

Adjacent sequences:  A305878 A305879 A305880 * A305882 A305883 A305884

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 13 2018

STATUS

approved

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Last modified May 31 09:30 EDT 2020. Contains 334748 sequences. (Running on oeis4.)