A347894 -id:A347894 - cp's OEIS frontend

A347817 E.g.f.: Product_{k>=1} (1 + x^k)^sin(x).

1, 0, 2, 3, 40, 80, 1760, 8211, 139256, 763272, 19466578, 147696835, 3372858476, 33370016316, 872184749046, 10340382875655, 289042962136272, 3884706041971728, 118640349946950738, 1911641854423398435, 59577007012206421356, 1086774235381609797540, 37138839666110194130670

Offset: 0

Seiichi Manyama, Sep 18 2021

nonn

Cf. A000593, A088311, A265024, A335629, A346841, A347893, A347894, A347898.

N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, (1+x^k)^sin(x))))

N=40; x='x+O('x^N); Vec(serlaplace(exp(sin(x)*sum(k=1, N, sigma(k>>valuation(k, 2))*x^k/k))))

E.g.f.: exp( sin(x) * Sum_{k>=1} x^k / (k*(1 - x^(2*k))) ). - Ilya Gutkovskiy, Sep 18 2021

E.g.f.: exp( sin(x) * Sum_{k>=1} A000593(k)*x^k/k ). - Seiichi Manyama, Sep 18 2021

A347893 E.g.f.: Product_{k>=1} (1 + x^k)^cos(x).

Original entry on oeis.org

1, 1, 2, 9, 30, 195, 1545, 12474, 95564, 1199397, 14287845, 167518846, 2341450386, 34489552331, 540927170147, 10114629115798, 175935142966408, 3184271322683385, 68623817313870153, 1442553498798565142, 31856896467060026670, 787164874800260366287, 19097783293834170329239

Offset: 0

Seiichi Manyama, Sep 18 2021

nonn

Cf. A000593, A265024, A346941, A347817, A347894, A347899.

N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, (1+x^k)^cos(x))))

N=40; x='x+O('x^N); Vec(serlaplace(exp(cos(x)*sum(k=1, N, sigma(k>>valuation(k, 2))*x^k/k))))

E.g.f.: exp( cos(x) * Sum_{k>=1} x^k / (k*(1 - x^(2*k))) ). - Ilya Gutkovskiy, Sep 18 2021

E.g.f.: exp( cos(x) * Sum_{k>=1} A000593(k)*x^k/k ). - Seiichi Manyama, Sep 18 2021

cp's OEIS Frontend

A347817 E.g.f.: Product_{k>=1} (1 + x^k)^sin(x).

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A347893 E.g.f.: Product_{k>=1} (1 + x^k)^cos(x).

Views

Author

Keywords

Crossrefs

Programs

PARI

PARI

Formula