A009405 Expansion of e.g.f. log(1+x)*cos(log(1+x)).

0, 1, -1, -1, 12, -76, 480, -3284, 24752, -205620, 1874340, -18639820, 201028080, -2337859200, 29162187600, -388263812000, 5492326876800, -82195910554800, 1296105033322800, -21449073720082000, 371056401062968000, -6682811910274568000, 124750905841882320000

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• Velin Yanev, Table of n, a(n) for n = 0..450

Programs

Mathematica

Table[n!*SeriesCoefficient[Log[x+1]*Cos[Log[x+1]],{x,0,n}],{n,0,20}] (* Velin Yanev, May 21 2024 *)
nmax = 20; CoefficientList[Series[Log[x+1]*Cos[Log[x+1]], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 29 2024 *)
RecurrenceTable[{(n^4+2*n^2+1)*a[n]+(4*n^3+6*n^2+8*n+3)*a[n+1]+3*(2*n^2+4*n+3)*a[n+2]+2*(2*n+3)*a[n+3]+a[n+4]==0,a[0]==0,a[1]==1,a[2]==-1,a[3]==-1},a,{n,20}] (* Velin Yanev, May 29 2024 *)

Formula

P-recursive sequence: (n^4 + 2*n^2 + 1)*a(n) + (4*n^3 + 6*n^2 + 8*n + 3)*a(n + 1) + 3*(2*n^2 + 4*n + 3)*a(n + 2) + 2*(2*n + 3)*a(n + 3) + a(n + 4) = 0. - Velin Yanev, May 28 2024

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997