A356667
Expansion of e.g.f. Sum_{k>=0} x^k / (1 - k*x^k/k!).
Original entry on oeis.org
1, 1, 4, 12, 72, 240, 2520, 10080, 127680, 816480, 11037600, 79833600, 1514177280, 12454041600, 261655954560, 2699348652000, 62869385779200, 711374856192000, 19407798693803520, 243290200817664000, 7300765959334848000, 102980278869910041600
Offset: 0
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a[n_]:= n! * DivisorSum[n, 1/(# - 1)!^(n/# - 1) &]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 22 2022 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(1-k*x^k/k!))))
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a(n) = if(n==0, 1, n!*sumdiv(n, d, 1/(d-1)!^(n/d-1)));
A358593
a(n) = n! * Sum_{d|n} d^(n-d) / d!^(n/d).
Original entry on oeis.org
1, 3, 7, 49, 121, 2701, 5041, 219521, 1587601, 33446701, 39916801, 17731796545, 6227020801, 2879710009177, 98069239768501, 2418218838097921, 355687428096001, 2832293713653708877, 121645100408832001, 2295597943489176040001, 71029619657111138063041
Offset: 1
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a[n_] := n! * DivisorSum[n, #^(n-#) / #!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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a(n) = n!*sumdiv(n, d, d^(n-d)/d!^(n/d));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!-(k*x)^k))))
A358594
Expansion of e.g.f. Sum_{k>0} x^k / ((k-1)! - x^k).
Original entry on oeis.org
1, 4, 9, 52, 125, 1626, 5047, 81768, 408249, 7263910, 39916811, 990191676, 6227020813, 174356750582, 1348633786515, 41861724727696, 355687428096017, 12904788209623614, 121645100408832019, 4866124222538035620, 51490090294307945301, 2248001455555300717294
Offset: 1
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a[n_] := n! * DivisorSum[n, 1/(#-1)!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/((k-1)!-x^k))))
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a(n) = n!*sumdiv(n, d, 1/(d-1)!^(n/d));
Showing 1-3 of 3 results.