A302583
a(n) = ((n + 1)^n - (n - 1)^n)/2.
Original entry on oeis.org
0, 1, 4, 28, 272, 3376, 51012, 908608, 18640960, 432891136, 11225320100, 321504185344, 10079828372880, 343360783937536, 12627774819845668, 498676704524517376, 21046391759976988928, 945381827279671853056, 45032132922921758270916, 2267322327322331161821184
Offset: 0
Cf.
A000169,
A065440,
A007778,
A062024,
A115416,
A274278,
A293022,
A302584,
A302585,
A302586,
A302587.
-
Table[((n + 1)^n - (n - 1)^n)/2, {n, 0, 19}]
nmax = 19; CoefficientList[Series[(x^2 - LambertW[-x]^2)/(2 x LambertW[-x] (1 + LambertW[-x])), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! SeriesCoefficient[Exp[n x] Sinh[x], {x, 0, n}], {n, 0, 19}]
A302587
a(n) = n! * [x^n] exp(n*x)*tanh(x).
Original entry on oeis.org
0, 1, 4, 25, 224, 2641, 38592, 671665, 13548544, 310580161, 7971353600, 226406902921, 7049219383296, 238722074157841, 8735529994928128, 343474252543881313, 14441163232204292096, 646510839624706118401, 30704150325602206089216, 1541807339347429264648441
Offset: 0
-
N:= 100: # to get a(0)..a(N)
T:= series(tanh(x),x,N+1):
C:= [seq(coeff(T,x,j),j=1..N)]:
seq(n! * add(C[i]*n^(n-i)/(n-i)!,i=1..n,2), n=0..N); # Robert Israel, Apr 10 2018
-
Table[n! SeriesCoefficient[Exp[n x] Tanh[x], {x, 0, n}], {n, 0, 19}]
-
a(n) = my(x='x+O('x^(n+1))); polcoeff(n!*exp(n*x)*tanh(x), n); \\ Michel Marcus, Apr 11 2018; corrected Jun 15 2022
A302584
a(n) = n! * [x^n] exp(n*x)/cos(x).
Original entry on oeis.org
1, 1, 5, 36, 357, 4500, 68857, 1239504, 25661545, 600655824, 15684383021, 452001644864, 14249852124365, 487836995500608, 18022519535240417, 714658089577017600, 30275849571771536977, 1364687729891761740032, 65213822241378992547925, 3293203845745202062590976
Offset: 0
-
Table[n! SeriesCoefficient[Exp[n x]/Cos[x], {x, 0, n}], {n, 0, 19}]
Table[(2 I)^n EulerE[n, (1 - I n)/2], {n, 0, 19}]
A302585
a(n) = n! * [x^n] exp(n*x)/cosh(x).
Original entry on oeis.org
1, 1, 3, 18, 165, 2000, 29855, 527632, 10762857, 248811264, 6428081979, 183537694208, 5739195739277, 195059957567488, 7159662639822615, 282252719348582400, 11894243092571825745, 533554809104057434112, 25384473065818477067123, 1276688324194885747474432
Offset: 0
-
Table[n! SeriesCoefficient[Exp[n x]/Cosh[x], {x, 0, n}], {n, 0, 19}]
Table[2^n EulerE[n, (n + 1)/2], {n, 0, 19}]
A302605
a(n) = n! * [x^n] exp(n*x)*arcsin(x).
Original entry on oeis.org
0, 1, 4, 28, 272, 3384, 51300, 917064, 18884672, 440168832, 11454902500, 329208395264, 10355322975120, 353851897861760, 13052503620917124, 516917167506777600, 21875427250996723968, 985164766018898243584, 47043119138733155306052, 2374168079889664129576960
Offset: 0
Cf.
A001818,
A115416,
A291482,
A293191,
A302583,
A302584,
A302585,
A302586,
A302587,
A302606,
A302608,
A302609.
-
Table[n! SeriesCoefficient[Exp[n x] ArcSin[x], {x, 0, n}], {n, 0, 19}]
A302609
a(n) = n! * [x^n] exp(n*x)*arctanh(x).
Original entry on oeis.org
0, 1, 4, 29, 288, 3649, 56160, 1017029, 21181440, 498682881, 13095232000, 379443829709, 12025239367680, 413761766695809, 15360425115176960, 611958601019294325, 26042588632355176448, 1179009749826940037889, 56579126414696034729984, 2868848293506101088635389
Offset: 0
Cf.
A010050,
A291484,
A293193,
A302583,
A302584,
A302585,
A302586,
A302587,
A302605,
A302606,
A302608.
-
Table[n! SeriesCoefficient[Exp[n x] ArcTanh[x], {x, 0, n}], {n, 0, 19}]
nmax = 20; CoefficientList[Series[Log[(1 - LambertW[-x])/(1 + LambertW[-x])] / (2*(1 + LambertW[-x])), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 09 2019 *)
A302606
a(n) = n! * [x^n] exp(n*x)*arcsinh(x).
Original entry on oeis.org
0, 1, 4, 26, 240, 2884, 42660, 748544, 15185856, 349574544, 9000902500, 256293989984, 7996078704240, 271246034903232, 9939835626507332, 391303051339622400, 16469438021801262848, 737992773619777599744, 35077254665501330210628, 1762671472887447792620032
Offset: 0
Cf.
A001818,
A002866,
A291483,
A302583,
A302584,
A302585,
A302586,
A302587,
A302605,
A302608,
A302609.
-
Table[n! SeriesCoefficient[Exp[n x] ArcSinh[x], {x, 0, n}], {n, 0, 19}]
A302608
a(n) = n! * [x^n] exp(n*x)*arctan(x).
Original entry on oeis.org
0, 1, 4, 25, 224, 2649, 38880, 679449, 13749248, 315919665, 8122432000, 231002307449, 7199799644160, 244028744225993, 8936047251296256, 351569799174274425, 14789182545666244608, 662389019735008588129, 31470659616611382460416, 1580849762199983023572313
Offset: 0
Cf.
A010050,
A279927,
A293192,
A302583,
A302584,
A302585,
A302586,
A302587,
A302605,
A302606,
A302609.
-
Table[n! SeriesCoefficient[Exp[n x] ArcTan[x], {x, 0, n}], {n, 0, 19}]
Join[{0}, Table[n^n (HypergeometricPFQ[{1, 1, 1 - n}, {2}, -(I/n)] + HypergeometricPFQ[{1, 1, 1 - n}, {2}, I/n])/2, {n, 19}]]
Showing 1-8 of 8 results.