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A003703 E.g.f. cos(log(1+x)).
(Formerly M2856)
5
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, Table of n, a(n) for n=0..100

Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565

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). [From 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);

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: A151077 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 November 24 01:09 EST 2014. Contains 249867 sequences.