A009218 Expansion of e.g.f. exp(sinh(log(1+x))).

1, 1, 0, 1, -2, 6, -14, -20, 876, -12572, 157816, -1953324, 24704560, -323390144, 4399642248, -62212681544, 912281561296, -13817130664560, 214872589110016, -3401627908578992, 54093656991247776, -844240783639323104

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Programs

Mathematica

With[{m = 21}, Range[0, m]! * CoefficientList[Series[Exp[ Sinh[ Log[ 1+x ] ] ], {x, 0, m}], x]]

Maxima

a[n]:=if n<3 then mod((n+1)^2,3) else (-2*n+3)*a[n-1]-(n-3)*(n-1)*a[n-2]+(n-1)*(n-2)*a[n-3]/2;
makelist(a[n],n,0,50); /* Tani Akinari, Feb 13 2024 */

PARI

my(x='x+O('x^35)); Vec(serlaplace(exp(sinh(log(1+x))))) \\ Joerg Arndt, Feb 13 2024

Formula

For n>2, a(n) = (-2*n+3)*a(n-1)-(n-3)*(n-1)*a(n-2)+(n-1)*(n-2)*a(n-3)/2. - Tani Akinari, Feb 13 2024

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Name clarified by Michel Marcus, Feb 13 2024