A294460 -id:A294460 - cp's OEIS frontend

A294459 E.g.f.: exp(-Sum_{n>=1} A001227(n) * x^n).

1, -1, -1, -7, 25, -41, 631, 881, 98897, -609265, 3798991, -41799671, 914146729, -15008576857, 16469525255, -5181463756351, 79515495724321, -1220435382764129, 12608713897126687, -449855614172366695, 10437031873016276921, -231918657853281955081

Offset: 0

Seiichi Manyama, Oct 31 2017

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Seiichi Manyama, Table of n, a(n) for n = 0..446

E.g.f.: exp(-Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): this sequence (k=0), A294460 (k=1), A294461 (k=2).

Cf. A018804.

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

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A001227(k)*a(n-k)/(n-k)! for n > 0.

E.g.f.: Product_{k>=1} 1 / (1 + x^k)^f(k), where f(k) = (1/k) * Sum_{j=1..k} gcd(k,j). - Ilya Gutkovskiy, Aug 17 2021

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Oct 31 2017

sign

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

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.

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

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

cp's OEIS Frontend

A294459 E.g.f.: exp(-Sum_{n>=1} A001227(n) * x^n).

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