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

1,2

Links

Table of n, a(n) for n=1..14.

Formula

a(n) = (2*n)! * Sum_{d|n} A000364(d) / (2*d)!.

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}]

Crossrefs

Cf. A000364, A028296, A176474, A330255, A330527.

Sequence in context: A158541 A114357 A142997 * A374230 A134940 A196676

Adjacent sequences: A330525 A330526 A330527 * A330529 A330530 A330531

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 17 2019

Status

approved