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A353170
Expansion of Product_{k>=1} (1 - x^k)^prime(k+1).
1
1, -3, -2, 7, 5, 9, -13, -27, -36, -36, 67, 117, 184, 171, -38, -356, -731, -883, -733, -90, 1194, 2828, 4202, 5008, 3993, 201, -6649, -15984, -26148, -32864, -30316, -13192, 22406, 75700, 139948, 196508, 222252, 184914, 53773, -192233, -547296, -968438, -1361207
OFFSET
0,2
COMMENTS
Convolution inverse of A353065.
MATHEMATICA
nmax = 42; CoefficientList[Series[Product[(1 - x^k)^Prime[k + 1], {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Sum[d Prime[d + 1], {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 28 2022
STATUS
approved