A073592 Euler transform of negative integers.
1, -1, -2, -1, 0, 4, 4, 7, 3, -2, -9, -17, -25, -24, -13, -1, 32, 61, 97, 111, 112, 74, 8, -108, -243, -392, -512, -569, -542, -358, -33, 473, 1078, 1788, 2395, 2865, 2955, 2569, 1496, -245, -2751, -5783, -9121, -12299, -14739, -15806, -14719, -10930, -3813, 6593, 20284, 36139, 53081, 68620, 80539
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vaclav Kotesovec)
- E. M. Wright, Coefficients of a reciprocal generating function, Quart. J. Math. 17 (1) (1966) 39-43, ADS Abstracts.
- N. J. A. Sloane, Transforms
Programs
-
Maple
a:= proc(n) option remember; `if`(n=0, 1, -add( numtheory[sigma][2](j)*a(n-j), j=1..n)/n) end: seq(a(n), n=0..60); # Alois P. Heinz, Mar 12 2015 -
Mathematica
nmax=50; CoefficientList[Series[Exp[Sum[-x^k/(k*(1-x^k)^2),{k,1,nmax}]],{x,0,nmax}],x] (* Vaclav Kotesovec, Mar 02 2015 *) a[n_]:= a[n] = -1/n*Sum[DivisorSigma[2,k]*a[n-k],{k,1,n}]; a[0]=1; Table[a[n],{n,0,100}] (* Vaclav Kotesovec, Mar 02 2015 *) -
SageMath
# uses[EulerTransform from A166861] b = EulerTransform(lambda n: -n) print([b(n) for n in range(55)]) # Peter Luschny, Nov 11 2020
Formula
G.f.: Product_{k>0} (1-x^k)^k.
a(n) = -1/n*Sum_{k=1..n} sigma[2](k)*a(n-k).
G.f.: exp( Sum_{n>=1} -sigma_2(n)*x^n/n ). - Seiichi Manyama, Mar 04 2017
Comments