A330528 Expansion of e.g.f. Sum_{k>=1} (sec(x^k) - 1) (even powers only).
1, 17, 421, 29945, 1864921, 382577645, 43788506581, 15558403000145, 3746015060385841, 1757547389533786325, 562069712763196977901, 516878970296221633758905, 201649817635812110915892361, 216661054181289983631892988285
Offset: 1
Keywords
Programs
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Mathematica
nmax = 14; Table[(CoefficientList[Series[Sum[(Sec[x^k] - 1), {k, 1, nmax}], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}] // Rest Table[(2 n)! DivisorSum[n, Abs[EulerE[2 #]]/(2 #)! &], {n, 1, 14}]
Formula
a(n) = (2*n)! * Sum_{d|n} A000364(d) / (2*d)!.