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}]
A115415
Real part of (n + i)^n, with i=sqrt(-1).
Original entry on oeis.org
1, 1, 3, 18, 161, 1900, 27755, 482552, 9722113, 222612624, 5707904499, 161981127968, 5039646554593, 170561613679808, 6237995487261915, 245159013138710400, 10303367499652761601, 461102348510408544512, 21891769059478538933603, 1098983344602124698522112
Offset: 0
-
Table[ Re[(n + I)^n], {n, 0, 17}] (* Robert G. Wilson v, Jan 23 2006 *)
-
a(n) = real((n + I)^n); \\ Michel Marcus, Apr 11 2018
-
from math import comb
def A115415(n): return sum(comb(n,j)*n**(n-j)*(-1 if j&2 else 1) for j in range(0,n+1,2)) # Chai Wah Wu, Feb 15 2024
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}]
A302586
a(n) = n! * [x^n] exp(n*x)*tan(x).
Original entry on oeis.org
0, 1, 4, 29, 288, 3641, 55872, 1008349, 20923392, 490730641, 12836633600, 370512824285, 11697136754688, 400947361714121, 14829211483455488, 588633245015433437, 24960134277040177152, 1126038686507284428961, 53851620649898789830656, 2721385807644104827095965
Offset: 0
-
Table[n! SeriesCoefficient[Exp[n x] Tan[x], {x, 0, n}], {n, 0, 19}]
Table[I^(n + 1) 2^(n - 1) (EulerE[n, (-I/2) n] - EulerE[n, 1 - (I/2) n]), {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}]
A370189
Imaginary part of (1 + n*i)^n, where i is the imaginary unit.
Original entry on oeis.org
0, 1, 4, -18, -240, 1900, 42372, -482552, -14970816, 222612624, 8825080100, -161981127968, -7809130867824, 170561613679808, 9678967816041188, -245159013138710400, -16000787866533953280, 461102348510408544512, 34017524842099233036996, -1098983344602124698522112, -90417110945911655996319600
Offset: 0
-
Array[Im[(1+#*I)^#] &, 25, 0] (* Paolo Xausa, Feb 19 2024 *)
-
a370189(n) = imag((1+I*n)^n)
-
from math import comb
def A370189(n): return sum(comb(n,j)*n**j*(-1 if j-1&2 else 1) for j in range(1,n+1,2)) # Chai Wah Wu, Feb 15 2024
A176302
a(n) = floor(abs( (i+n)^n )) where "i" is the Imaginary unit.
Original entry on oeis.org
1, 5, 31, 289, 3446, 50653, 883883, 17850625, 409413666, 10510100501, 298523873866, 9294114390625, 314715395761089, 11514990476898413, 452702917746710142, 19031147999601100801, 851888944448164153708
Offset: 1
-
C := ComplexField(); [Floor(Abs( (n+I)^n )): n in [1..30]]; // G. C. Greubel, Nov 26 2019
-
seq(floor(abs((n+I)^n)), n = 1..30); # G. C. Greubel, Nov 26 2019
-
Table[Floor@Abs[(I + n)^n], {n,30}]
-
default(realprecision, 50); vector(30, n, (abs((I+n)^n))\1 ) \\ G. C. Greubel, Nov 26 2019
-
[floor(abs( (n+i)^n )) for n in (1..30)] # G. C. Greubel, Nov 26 2019
Showing 1-7 of 7 results.
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