A354546 Expansion of e.g.f. exp(x)^( cos(x) - sin(x) ).

1, 1, -1, -8, -7, 96, 385, -1210, -14943, -5912, 593361, 2409298, -22935647, -236575468, 590041257, 20313729886, 40488350401, -1659176093392, -11796304552991, 120680593857514, 1966312603184321, -4949789957167124, -288454178376442407, -849587090710029098

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^floor(k/2) * k * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)^(cos(x)-sin(x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^(j\2)*j*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A000248, A009189, A009214, A354545.

Sequence in context: A237646 A288188 A038285 * A261117 A098432 A197623

Adjacent sequences: A354543 A354544 A354545 * A354547 A354548 A354549

Keyword

sign

Author

Seiichi Manyama, Aug 18 2022

Status

approved