A335980
Expansion of e.g.f. exp(2 * (1 - exp(-x)) + x).
Original entry on oeis.org
1, 3, 7, 11, 7, -5, 23, 75, -281, -101, 4663, -14229, -41721, 532667, -1464489, -8840053, 103689511, -313202725, -2348557705, 32041266859, -127039882425, -762423051013, 14393151011735, -81523161874741, -236027974047897, 8564406463119387
Offset: 0
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nmax = 25; CoefficientList[Series[Exp[2 (1 - Exp[-x]) + x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = a[n - 1] + 2 Sum[(-1)^(n - k - 1) Binomial[n - 1, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 25}]
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my(N=33, x='x+O('x^N)); Vec(serlaplace(exp(2 * (1 - exp(-x)) + x))) \\ Joerg Arndt, Jul 04 2020
A335982
Expansion of e.g.f. exp(4 * (1 - exp(-x)) + x).
Original entry on oeis.org
1, 5, 21, 69, 149, 69, -619, -187, 9365, -3515, -193643, 453957, 4704917, -29425595, -83918443, 1640246085, -3184430955, -74516517307, 604223657877, 1324972362053, -52526078298475, 264984579390533, 2477371363954069, -44206576595187899, 133280843118435477
Offset: 0
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nmax = 24; CoefficientList[Series[Exp[4 (1 - Exp[-x]) + x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = a[n - 1] + 4 Sum[(-1)^(n - k - 1) Binomial[n - 1, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]
A320432
Expansion of e.g.f. exp(3 * (1 - exp(x)) + x).
Original entry on oeis.org
1, -2, 1, 7, -8, -65, 37, 1024, 1351, -19001, -92618, 232513, 4087189, 9953926, -123909155, -1170342533, -676144160, 62840385619, 490129709977, -551829062288, -40624407525941, -305175084654341, 698633855671510, 34571970743398621, 278738497423756153, -663168571756087538
Offset: 0
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m = 25; Range[0, m]! * CoefficientList[Series[Exp[3 * (1 - Exp[x]) + x], {x, 0, m}], x] (* Amiram Eldar, Jul 06 2020 *)
Table[Sum[Binomial[n, k] * BellB[k, -3], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 06 2020 *)
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N=40; x='x+O('x^N); Vec(serlaplace(exp(3*(1-exp(x))+x)))
Showing 1-3 of 3 results.