A296336 Expansion of e.g.f. log(1 + x*cos(x))*exp(x).

0, 1, 1, -1, 0, -16, -5, 13, -1512, 12336, -98177, 444773, 1249160, -75244508, 1296229779, -15956614403, 130892534160, 59122803744, -31478991643617, 837166840532589, -14900078660739984, 181343532181629332, -480411914937891389, -54306065912649098539, 2080183542455901881320

Offset

0,6

Links

Table of n, a(n) for n=0..24.

Example

log(1 + x*cos(x))*exp(x) = x/1! + x^2/2! - x^3/3! - 16*x^5/5! - 5*x^6/6! + ...

Maple

a:=series(log(1 + x*cos(x))*exp(x), x=0, 25): seq(n!*coeff(a, x, n), n=0..24); # Paolo P. Lava, Mar 27 2019

Mathematica

nmax = 24; CoefficientList[Series[Log[1 + x Cos[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) x='x+O('x^99); concat([0], Vec(serlaplace(exp(x)*log(1+x*cos(x))))) \\ Altug Alkan, Dec 28 2017

Crossrefs

Cf. A003728, A009334, A009371, A294314, A295278, A296436, A296438, A297206.

Sequence in context: A336782 A040245 A070538 * A198064 A233000 A070581

Adjacent sequences: A296333 A296334 A296335 * A296337 A296338 A296339

Keyword

sign

Author

Ilya Gutkovskiy, Dec 27 2017

Status

approved