A368271
Expansion of e.g.f. exp(2*x) / (1 + x*exp(x)).
Original entry on oeis.org
1, 1, 0, -1, 4, 7, -74, 23, 2136, -7345, -77006, 712879, 2499124, -69799897, 88342398, 7311735143, -50617554896, -762825930977, 12821702643946, 56041362405119, -2956159258069044, 8447845572175031, 660257137187089270, -7376306690095890185
Offset: 0
A375627
Expansion of e.g.f. exp(2*x^2) / (1 - x * exp(x^2)).
Original entry on oeis.org
1, 1, 6, 24, 168, 1260, 11760, 126000, 1545600, 21304080, 326350080, 5497873920, 101048048640, 2011924474560, 43139969832960, 991088998099200, 24286975237324800, 632358338278867200, 17433184834127462400, 507307459608530380800, 15539683835941532467200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^2)/(1-x*exp(x^2))))
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a(n) = n!*sum(k=0, n\2, (n-2*k+2)^k/k!);
A368266
Expansion of e.g.f. exp(-2*x) / (1 - x*exp(x)).
Original entry on oeis.org
1, -1, 4, 1, 60, 393, 4498, 54689, 773384, 12268369, 216328614, 4195769433, 88776964444, 2034936319817, 50232646818890, 1328570248040497, 37481046375146640, 1123486426007081505, 35657224567565828302, 1194561018775753556777, 42125545306641497600036
Offset: 0
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CoefficientList[Series[Exp[-2*x]/ (1 - x*Exp[x]),{x,0,20}],x]Range[0,20]! (* Stefano Spezia, Feb 21 2025 *)
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a(n) = n!*sum(k=0, n, (n-k-2)^k/k!);
A375629
Expansion of e.g.f. exp(2*x) / (1 - x^2 * exp(x)).
Original entry on oeis.org
1, 2, 6, 26, 148, 1052, 8974, 89294, 1015480, 12991832, 184682554, 2887850858, 49261993444, 910356170804, 18117379906630, 386315966673638, 8786555389140976, 212335975835710256, 5433155029435593970, 146744457899073450050, 4172032796528725318876
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^2*exp(x))))
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a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(n-2*k)!);
A375628
Expansion of e.g.f. exp(2*x^3) / (1 - x * exp(x^3)).
Original entry on oeis.org
1, 1, 2, 18, 96, 600, 5760, 57960, 645120, 8285760, 117936000, 1842825600, 31374604800, 578334556800, 11493004723200, 244720360684800, 5555523785011200, 134002274473267200, 3422904611167641600, 92290617116425728000, 2619214995575033856000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^3)/(1-x*exp(x^3))))
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a(n) = n!*sum(k=0, n\3, (n-3*k+2)^k/k!);
A375630
Expansion of e.g.f. exp(2*x) / (1 - x^3 * exp(x)).
Original entry on oeis.org
1, 2, 4, 14, 88, 572, 4024, 37298, 404464, 4601528, 58426864, 846080798, 13209174136, 219868220756, 3981563464792, 77708414601098, 1606665377716576, 35246223612156272, 821962294211430496, 20227931586257247542, 522932344617513862696, 14204133017700173041292
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^3*exp(x))))
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a(n) = n!*sum(k=0, n\3, (k+2)^(n-3*k)/(n-3*k)!);
A375631
Expansion of e.g.f. exp(2*x) / (1 - x^2/2 * exp(x)).
Original entry on oeis.org
1, 2, 5, 17, 76, 422, 2809, 21821, 193708, 1934468, 21465529, 262007033, 3488768650, 50326173458, 781808322481, 13012772925293, 231029881905736, 4358082011900744, 87045479653871377, 1835177785479753545, 40727378713879346206, 949039029924830652662
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^2/2*exp(x))))
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a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(2^k*(n-2*k)!));
A375632
Expansion of e.g.f. exp(2*x) / (1 - x^3/6 * exp(x)).
Original entry on oeis.org
1, 2, 4, 9, 28, 122, 624, 3523, 22824, 170948, 1422664, 12856373, 126598036, 1358773886, 15721899652, 194356158823, 2560950546576, 35899907132872, 533099244285136, 8351271711094697, 137675784924101596, 2383758487476054242, 43244905386257120044
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^3/6*exp(x))))
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a(n) = n!*sum(k=0, n\3, (k+2)^(n-3*k)/(6^k*(n-3*k)!));
Showing 1-8 of 8 results.