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

0,3

Links

Table of n, a(n) for n=0..22.

Example

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! + ...

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

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}]

Crossrefs

Cf. A000364, A003701, A004211, A009006, A009212, A009248, A009268, A305708.

Sequence in context: A039302 A074512 A005502 * A351200 A000255 A318912

Adjacent sequences: A305707 A305708 A305709 * A305711 A305712 A305713

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 08 2018

Status

approved