A353170 Expansion of Product_{k>=1} (1 - x^k)^prime(k+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.

Links

Table of n, a(n) for n=0..42.

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

Cf. A007441, A065091, A353065, A353169.

Sequence in context: A069888 A073281 A130922 * A263018 A372744 A215622

Adjacent sequences: A353167 A353168 A353169 * A353171 A353172 A353173

Keyword

sign

Author

Ilya Gutkovskiy, Apr 28 2022

Status

approved