A352278 a(0) = 1; a(n) = -3 * Sum_{k=1..n} binomial(2*n-1,2*k-1) * a(n-k).
1, -3, 24, -273, 3399, -31728, -280371, 26388177, -580539936, -17406321933, 1809690920979, -18045563411208, -6249108953966151, 333062472085204677, 27673022056089337224, -3800202930423874873353, -139584280492439116159521, 52779027474493111545620352, 279012844299708383976573189
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = -3 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[3 (1 - Cosh[x])], {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]
Formula
E.g.f.: exp( 3 * (1 - cosh(x)) ) (even powers only).