A305710 Expansion of e.g.f. exp(sec(x)*exp(x) - 1).
1, 1, 3, 11, 53, 297, 1959, 14499, 120409, 1097025, 10931771, 117685163, 1363889133, 16887554569, 222672557631, 3110742121059, 45912214062961, 713290136581697, 11636755988405555, 198800967493444875, 3549276499518132325, 66076184834921382313, 1280502976522048458647
Offset: 0
Keywords
Examples
exp(sec(x)*exp(x) - 1) = 1 + x + 3*x^2/2! + 11*x^3/3! + 53*x^4/4! + 297*x^5/5! + 1959*x^6/6! + 14499*x^7/7! + ...
Programs
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Maple
a:=series(exp(sec(x)*exp(x)-1),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # Paolo P. Lava, Mar 26 2019
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Mathematica
nmax = 22; CoefficientList[Series[Exp[Sec[x] Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]! a[n_] := a[n] = Sum[(2 I)^k EulerE[k, 1/2 - I/2] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 22}]