A364822 Expansion of e.g.f. cosh(x) / (1 - 2*sinh(x)).
1, 2, 9, 56, 465, 4832, 60249, 876416, 14570145, 272502272, 5662834089, 129446475776, 3228012339825, 87205172928512, 2537079010567929, 79084060649947136, 2629496833837277505, 92893490657046167552, 3474733464040954877769, 137195165161622584426496, 5702069567580948171751185
Offset: 0
Keywords
Links
- Paul Kinlaw, Michael Morris, and Samanthak Thiagarajan, Sums related to the Fibonacci sequence, Husson University (2021). See Table 2 p. 5.
Programs
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Maple
a := n -> add(binomial(n,2*k)*add(j!*combinat[fibonacci](j+2)*Stirling2(n-2*k,j), j=0..n-2*k), k=0..floor(n/2)): seq(a(n), n = 0 .. 20); # second program: b := proc(n) option remember; `if`(n = 0, 1, 2+2*add(binomial(n,2*k-1)*b(n-2*k+1), k=1..floor((n+1)/2))) end: a := proc(n) `if`(n = 0, 1, b(n)/2) end: seq(a(n), n = 0 .. 20); # third program: (1/2)*((exp(-x) + exp(x))/(1 + exp(-x) - exp(x))): series(%, x, 21): seq(n!*coeff(%, x, n), n = 0..20); # Peter Luschny, Nov 07 2023
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Mathematica
a[n_]:=n!*SeriesCoefficient[Cosh[x]/(1 - 2*Sinh[x]),{x,0,n}]; Array[a,21,0] (* Stefano Spezia, Nov 07 2023 *) -
PARI
my(x='x+O('x^30)); Vec(serlaplace(cosh(x) / (1 - 2*sinh(x)))) \\ Michel Marcus, Nov 07 2023
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