A294459 -id:A294459

Search: a294459 -id:a294459

Displaying 1-3 of 3 results found.

page 1

A294460

E.g.f.: exp(-Sum_{n>=1} A000593(n) * x^n).

+10
3

1, -1, -1, -19, 73, -401, 5191, -29779, 879089, -7232833, 103048111, -1891058291, 31696845049, -649348332049, 9310670445623, -270217657103731, 5480877008565601, -131578355696804609, 3133521575795986399, -81890613282163881043, 2460096066325021029161

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..437

FORMULA

a(0) = 1 and a(n) = (-1) * (n-1)! * Sum_{k=1..n} k*A000593(k)*a(n-k)/(n-k)! for n > 0.

PROG

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

CROSSREFS

E.g.f.: exp(-Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): A294459 (k=0), this sequence (k=1), A294461 (k=2).

Cf. A000593, A081362, A294394.

KEYWORD

sign

AUTHOR

Seiichi Manyama, Oct 31 2017

STATUS

approved

A294461

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

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

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

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.

PROG

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

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.

KEYWORD

sign

AUTHOR

Seiichi Manyama, Oct 31 2017

STATUS

approved

A294458

E.g.f.: Product_{n>=1} (1 - x^(2*n-1))^(1/(2*n-1)).

+10
1

1, -1, 0, -2, 8, -24, 64, -160, 8448, -86912, 509696, -1449216, 44615680, -366395392, 3315376128, -190488356864, 4591008579584, -33244620718080, 86342088982528, -2543409132470272, 136456182420996096, -5644134983026343936, 103753337226615848960

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..450

FORMULA

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

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

PROG

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

CROSSREFS

Cf. A081362, A206303, A285069, A294459.

KEYWORD

sign

AUTHOR

Seiichi Manyama, Oct 31 2017

STATUS

approved

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