A351929
Expansion of e.g.f. exp(x - x^3/6).
Original entry on oeis.org
1, 1, 1, 0, -3, -9, -9, 36, 225, 477, -819, -10944, -37179, 16875, 870507, 4253796, 2481921, -101978919, -680495175, -1060229088, 16378166061, 145672249311, 368320357791, -3415036002300, -40270115077983, -141926533828299, 882584266861701, 13970371667206176
Offset: 0
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m = 27; Range[0, m]! * CoefficientList[Series[Exp[x - x^3/6], {x, 0, m}], x] (* Amiram Eldar, Feb 26 2022 *)
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my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x-x^3/6)))
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a(n) = n!*sum(k=0, n\3, (-1/3!)^k*binomial(n-2*k, k)/(n-2*k)!);
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a(n) = if(n<3, 1, a(n-1)-binomial(n-1, 2)*a(n-3));
A351906
Expansion of e.g.f. exp(x * (1 - x^4)).
Original entry on oeis.org
1, 1, 1, 1, 1, -119, -719, -2519, -6719, -15119, 1784161, 19902961, 119655361, 518763961, 1815974161, -212497445159, -3472602456959, -29605333299359, -177764320560959, -844590032480159, 97992221659873921, 2116963290135836521, 23379513665735470321
Offset: 0
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my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-x^4))))
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a(n) = n!*sum(k=0, n\5, (-1)^k*binomial(n-4*k, k)/(n-4*k)!);
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a(n) = if(n<5, 1, a(n-1)-5!*binomial(n-1, 4)*a(n-5));
A351905
Expansion of e.g.f. exp(x * (1 - x^3)).
Original entry on oeis.org
1, 1, 1, 1, -23, -119, -359, -839, 18481, 178417, 902161, 3318481, -69866279, -1011908039, -7204341143, -36194591159, 726745175521, 14326789219681, 131901636673441, 840736509931297, -16060449291985079, -408041402342457239, -4618341644958693959, -35691963052019431079
Offset: 0
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my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-x^3))))
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a(n) = n!*sum(k=0, n\4, (-1)^k*binomial(n-3*k, k)/(n-3*k)!);
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a(n) = if(n<4, 1, a(n-1)-4!*binomial(n-1, 3)*a(n-4));
A362309
Expansion of e.g.f. exp(x - x^3/3).
Original entry on oeis.org
1, 1, 1, -1, -7, -19, 1, 211, 1009, 953, -14239, -105049, -209879, 1669669, 18057313, 56255291, -294375199, -4628130319, -19929569471, 70149241423, 1652969810521, 9226206209501, -20236475188159, -783908527648861, -5452368869656367
Offset: 0
Showing 1-4 of 4 results.