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

0,3

Comments

1/A(x) is g.f. for A000219.

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

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

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 *)

Prog

(SageMath) # uses[EulerTransform from A166861]
b = EulerTransform(lambda n: -n)
print([b(n) for n in range(55)]) # Peter Luschny, Nov 11 2020

Crossrefs

Column k=1 of A283272.

Cf. A000219, A001157, A001478, A026007, A156616, A255528.

Sequence in context: A109167 A066426 A100887 * A164994 A269952 A361954

Adjacent sequences: A073589 A073590 A073591 * A073593 A073594 A073595

Keyword

sign

Author

Vladeta Jovovic, Aug 28 2002

Status

approved