A009537 Expansion of sin(x)*cosh(log(1+x)).

0, 1, 0, 2, -12, 51, -300, 2120, -16968, 152677, -1526760, 16794414, -201532980, 2619928663, -36679001268, 550185019124, -8802960306000, 149650325201865, -2693705853633552, 51180411219037658, -1023608224380753180

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..449

Formula

a(n) ~ n! * (-1)^(n+1) * sin(1) / 2. - Vaclav Kotesovec, Jan 23 2015

From Robert Israel, Jan 07 2019: (Start)

E.g.f.: sin(x)*(1+x+1/(1+x))/2.

a(2*k) = (-1)^(k+1)*k - (2*k)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).

a(2*k+1) = (-1)^k + (2*k+1)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).

(End)

Maple

S:= series(sin(x)*(1+x+1/(1+x))/2, x, 51):
seq(coeff(S, x, j)*j!, j=0..50); # Robert Israel, Jan 07 2019

Mathematica

With[{nn=20}, CoefficientList[Series[Sin[x]*Cosh[Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 20 2015 *)
CoefficientList[Series[((1 + (1 + x)^2)*Sin[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)

Crossrefs

Sequence in context: A359523 A323851 A054667 * A057547 A216648 A043007

Adjacent sequences: A009534 A009535 A009536 * A009538 A009539 A009540

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Aug 20 2015

Status

approved