A294461 E.g.f.: exp(-Sum_{n>=1} A050999(n) * x^n).

1, -1, -1, -55, 217, -2441, 41911, -343519, 10531025, -123024817, 2722259791, -64395229031, 1218005521129, -36874422541945, 785879799954887, -25331247487596751, 708096286059632161, -21422225147712360929, 741754828422824400415

Offset: 0

Author

Seiichi Manyama, Oct 31 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..424

Crossrefs

E.g.f.: exp(-Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): A294459 (k=0), A294460 (k=1), this sequence (k=2).

Cf. A050999, A285069, A294395.

Programs

PARI

N=66; x='x+O('x^N); Vec(serlaplace(exp(-sum(k=1, N, sumdiv(k, d, d^2*(d%2))*x^k))))

Formula

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A050999(k)*a(n-k)/(n-k)! for n > 0.