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A002742 Logarithmic numbers.
(Formerly M1672 N0658)
3
2, -6, 24, -80, 450, -2142, 17696, -112464, 1232370, -9761510, 132951192, -1258797696, 20476388114, -225380451870, 4261074439680, -53438049741152, 1151146814425506, -16199301256675974, 391615698778725080, -6109914386833902960 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

J. M. Gandhi, On logarithmic numbers, Math. Student, 31 (1963), 73-83. [Annotated scanned copy]

Index entries for sequences related to logarithmic numbers

FORMULA

E.g.f.: (2*x/(1-x^2)+log(1-x^2))*exp(-x). - Sean A. Irvine, Aug 11 2014

a(n) = 2*A002747(n) - a(n-1). - R. J. Mathar, Jul 24 2015

From Emanuele Munarini, Dec 16 2017: (Start)

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

a(n+3)+a(n+2)-(n+2)*(n+3)*a(n+1)-(n+2)*(n+3)*a(n) = 2*(-1)^n*(n+3).

(n+3)*a(n+4)+(2*n+7)*a(n+3)-(n+2)*(n+4)^2*a(n+2)-(n+3)*(n+4)*(2*n+5)*a(n+1)-(n+2)*(n+3)*(n+4)*a(n) = 0.

E.g.f.: A(x) = - D(exp(-x)*log(1-x^2)), where D is the derivative with respect to x. (End)

a(n) ~ n! * (exp(-1) - (-1)^n * exp(1)). - Vaclav Kotesovec, Dec 16 2017

MATHEMATICA

Table[(-1)^(n-1)Sum[Binomial[n+1, 2k+1](n-2k)/(k+1)(2k+1)!, {k, 0, n}], {n, 0, 100}] (* Emanuele Munarini, Dec 16 2017 *)

PROG

(Maxima) makelist((-1)^(n-1)*sum(binomial(n+1, 2*k+1)*(n-2*k)/(k+1)*(2*k+1)!, k, 0, n), n, 0, 12); /* Emanuele Munarini, Dec 16 2017 */

(PARI) first(n) = x='x+O('x^(n+1)); Vec(serlaplace((2*x/(1-x^2)+log(1-x^2))*exp(-x))) \\ Iain Fox, Dec 16 2017

CROSSREFS

Cf. A002741.

Sequence in context: A095110 A189858 A189568 * A048120 A322198 A003759

Adjacent sequences:  A002739 A002740 A002741 * A002743 A002744 A002745

KEYWORD

sign

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Jeffrey Shallit

More terms from Sean A. Irvine, Aug 11 2014

STATUS

approved

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Last modified May 8 15:03 EDT 2021. Contains 343666 sequences. (Running on oeis4.)