A352277 a(0) = 1; a(n) = -2 * Sum_{k=1..n} binomial(2*n-1,2*k-1) * a(n-k).
1, -2, 10, -62, 250, 3538, -109430, 376738, 64406170, -1496149262, -66387156950, 4120939699138, 114360544465210, -16447057086702062, -315993884108535350, 99921676927889325538, 1478937314465295441370, -907773678752741550637262, -14225447208333541085396630
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = -2 Sum[Binomial[2 n - 1, 2 k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}] nmax = 36; Take[CoefficientList[Series[Exp[2 (1 - Cosh[x])], {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]
Formula
E.g.f.: exp( 2 * (1 - cosh(x)) ) (even powers only).