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A003703 E.g.f. cos(log(1+x)).
(Formerly M2856)
8
1, 0, -1, 3, -10, 40, -190, 1050, -6620, 46800, -365300, 3103100, -28269800, 271627200, -2691559000, 26495469000, -238131478000, 1394099824000, 15194495654000, -936096296850000, 29697351895900000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

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

LINKS

T. D. Noe and Vaclav Kotesovec, Table of n, a(n) for n = 0..400 (first 100 terms from T. D. Noe)

Vaclav Kotesovec, Graph a(n+1)/a(n)

Vladimir Victorovich Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

FORMULA

a(n) = sum{k=0..n-1, (-1)^(k+1)*T(n-k, k)*sin(pi*(n-k-1)/2)}+0^n; T(n, k)=abs(A008276(n, k)). - Paul Barry, Apr 18 2005

abs(a(n)) = abs(f(n)) with f(n)=prod(i+k,k=1..n) (where i^2=-1). - Yalcin Aktar, Jul 13 2009

a(n) = Sum_{k=0..floor(n/2)} stirling1(n,2*k)*(-1)^(k). - Vladimir Kruchinin, Jan 29 2011

a(n+2)= -a(n+1)*(2*n+1) - a(n)*(1+n^2), a(0)=1, a(1)=0. - Sergei N. Gladkovskii, Aug 17 2012

EXAMPLE

1 - x^2 + 3*x^3 - 10*x^4 + 40*x^5 - 190*x^6 + 1050*x^7 - 6620*x^8 + ...

MAPLE

a:= n-> add (combinat[stirling1](n, 2*k) * (-1)^(k), k=0..floor(n/2)):

seq (a(n), n=0..20);

MATHEMATICA

CoefficientList[Series[Cos[Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 16 2015 *)

Table[(-1)^n Im[Pochhammer[1-I, n-1]], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 13 2016 *)

PROG

(PARI) {a(n) = if( n<0, 0, n! * polcoeff( cos( log( 1 + x + x * O(x^n))), n))} /* Michael Somos, Jul 26 2012 */

CROSSREFS

Cf. A009024, A009454.

Sequence in context: A258973 A217885 A216367 * A242651 A231531 A136128

Adjacent sequences:  A003700 A003701 A003702 * A003704 A003705 A003706

KEYWORD

easy,sign

AUTHOR

R. H. Hardin, Simon Plouffe

STATUS

approved

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Last modified December 9 17:46 EST 2016. Contains 278985 sequences.