A295122 Expansion of Product_{k>=1} 1/(1 + x^k)^(k*(5*k-3)/2).

1, -1, -6, -12, 6, 65, 179, 202, -137, -1392, -3492, -5135, -1325, 15437, 52934, 101787, 116827, -16945, -462603, -1350732, -2475989, -2889620, -343236, 8559858, 26972213, 53099230, 72521956, 47535918, -86985043, -409729146, -952305325, -1577038736

Offset: 0

Author

Seiichi Manyama, Nov 15 2017

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = n*(5*n-3)/2, g(n) = -1.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A294846 (b=3), A284896 (b=4), A295086 (b=5), A295121 (b=6), this sequence (b=7), A295123 (b=8).

Programs

PARI

N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1+x^k)^(k*(5*k-3)/2)))

Formula

Convolution inverse of A294837.

G.f.: Product_{k>=1} 1/(1 + x^k)^A000566(k).

a(0) = 1 and a(n) = (1/(2*n)) * Sum_{k=1..n} b(k)*a(n-k) where b(n) = Sum_{d|n} d^2*(5*d-3)*(-1)^(n/d).