A336950
E.g.f.: 1 / (1 - x * exp(2*x)).
Original entry on oeis.org
1, 1, 6, 42, 392, 4600, 64752, 1063216, 19952256, 421227648, 9880951040, 254960721664, 7176891675648, 218857588139008, 7187394935347200, 252897556424140800, 9491754142468702208, 378509920569294684160, 15982018774576565649408, 712306819507400060502016
Offset: 0
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nmax = 19; CoefficientList[Series[1/(1 - x Exp[2 x]), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[n! Sum[(2 (n - k))^k/k!, {k, 0, n}], {n, 1, 19}]]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k 2^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
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seq(n)={ Vec(serlaplace(1 / (1 - x*exp(2*x + O(x^n))))) } \\ Andrew Howroyd, Aug 08 2020
A336948
E.g.f.: 1 / (exp(-3*x) - x).
Original entry on oeis.org
1, 4, 23, 195, 2229, 31863, 546255, 10925757, 249753897, 6422808411, 183524701779, 5768419379913, 197791542799965, 7347180526444359, 293912722687075767, 12597352573293062757, 575928946256877156177, 27976119070974574461363, 1438896686251112024068251
Offset: 0
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nmax = 18; CoefficientList[Series[1/(Exp[-3 x] - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(3 (n - k + 1))^k/k!, {k, 0, n}], {n, 0, 18}]
a[0] = 1; a[n_] := a[n] = 4 n a[n - 1] - Sum[Binomial[n, k] (-3)^k a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 18}]
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seq(n)={ Vec(serlaplace(1 / (exp(-3*x + O(x*x^n)) - x))) } \\ Andrew Howroyd, Aug 08 2020
A368236
Expansion of e.g.f. 1/(exp(-x) - 2*x).
Original entry on oeis.org
1, 3, 17, 145, 1649, 23441, 399865, 7957881, 180997857, 4631289697, 131670338921, 4117813225769, 140486274499345, 5192341564319313, 206669931188282073, 8813624820931402201, 400922608851086766017, 19377398675442025382081, 991639882680576890150089
Offset: 0
A336949
a(n) = n! * [x^n] 1 / (exp(-n*x) - x).
Original entry on oeis.org
1, 2, 14, 195, 4440, 147745, 6698448, 394852577, 29250137472, 2652483234033, 288363456748800, 36952298766628465, 5504130616452258816, 941845623036360908489, 183298110723156455921664, 40221612394630225987208625, 9876429434585097671993032704
Offset: 0
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Table[n! SeriesCoefficient[1/(Exp[-n x] - x), {x, 0, n}], {n, 0, 16}]
Join[{1}, Table[n! Sum[(n (n - k + 1))^k/k!, {k, 0, n}], {n, 1, 16}]]
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a(n)={n!*polcoef(1/(exp(-n*x + O(x*x^n)) - x), n)} \\ Andrew Howroyd, Aug 08 2020
A336958
E.g.f.: 1 / (exp(2*x) - x).
Original entry on oeis.org
1, -1, -2, 10, 24, -312, -560, 19472, 6272, -1994624, 4072704, 299059968, -1635814400, -60723321856, 628215191552, 15716076562432, -274420622327808, -4900668238036992, 140182198527655936, 1717697481518809088, -83651335147070685184, -590374211868638314496
Offset: 0
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nmax = 21; CoefficientList[Series[1/(Exp[2 x] - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(-2 (n - k + 1))^k/k!, {k, 0, n}], {n, 0, 21}]
a[0] = 1; a[n_] := a[n] = -n a[n - 1] - Sum[Binomial[n, k] 2^k a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 21}]
Showing 1-5 of 5 results.