A294392
E.g.f.: exp(Sum_{n>=1} A001227(n) * x^n).
Original entry on oeis.org
1, 1, 3, 19, 97, 801, 7411, 73123, 821409, 10977697, 151612291, 2286137811, 38308830913, 669163118209, 12649211055027, 257559356068771, 5432325991339201, 121949878889492673, 2907330680764076419, 71860237654425159187, 1871308081194213959841
Offset: 0
E.g.f.: exp(Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n): this sequence (k=0),
A294394 (k=1),
A294395 (k=2).
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a[n_] := a[n] = If[n == 0, 1, Sum[k*DivisorSum[k, Mod[#, 2] &]*a[n - k], {k, 1, n}]/n]; Table[n!*a[n], {n, 0, 20}] (* Vaclav Kotesovec, Sep 07 2018 *)
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N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, d%2)*x^k))))
A294394
E.g.f.: exp(Sum_{n>=1} A000593(n) * x^n).
Original entry on oeis.org
1, 1, 3, 31, 145, 1641, 17731, 194503, 2676801, 40644145, 667689571, 11514903951, 227665389073, 4578990563161, 100913115588195, 2372334731747191, 57930324367791361, 1509398686720812513, 41341036374519788611, 1184009909077133031295
Offset: 0
E.g.f.: exp(Sum_{n>=1} (Sum_{d|n and d is odd} d^k) * x^n):
A294392 (k=0), this sequence (k=1),
A294395 (k=2).
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a[n_] := a[n] = If[n == 0, 1, Sum[k*Sum[-(-1)^d*k/d, {d, Divisors[k]}]*a[n - k], {k, 1, n}]/n]; Table[n!*a[n], {n, 0, 20}] (* Vaclav Kotesovec, Sep 07 2018 *)
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N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, d*(d%2))*x^k))))
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
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).
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N=66; x='x+O('x^N); Vec(serlaplace(exp(-sum(k=1, N, sumdiv(k, d, d^2*(d%2))*x^k))))
Showing 1-3 of 3 results.