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A003709 E.g.f. cos(sin(x)) (even powers only).
(Formerly M3986)
4
1, -1, 5, -37, 457, -8169, 188685, -5497741, 197920145, -8541537105, 432381471509, -25340238127989, 1699894200469849, -129076687233903673, 10989863562589199389, -1041327644107761435101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of ways to partition the set {1,2,...,2n} into an even number of odd size blocks. - Geoffrey Critzer, Apr 11 2010

Unsigned sequence has e.g.f. cosh(sinh(x)) (even powers only).

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 8th line of table.

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..50

FORMULA

a(n) = sum(j=0..n, (2^(2*j+1)*sum(i=0..(n-j), (i-n+j)^(2*n)*binomial((2*n-2*j),i)*(-1)^(n-i))/(2*n-2*j)!)), n>0, a(1)=0. - Vladimir Kruchinin, Jun 08 2011

MATHEMATICA

Take[With[{nn=40}, CoefficientList[Series[Cos[Sin[x]], {x, 0, nn}], x] Range[0, nn]!], {1, -1, 2}] (* Harvey P. Dale, Sep 18 2011 *)

PROG

(Maxima)

a(n):=sum((2^(2*j+1)*sum((i-n+j)^(2*n)*binomial((2*n-2*j), i)*(-1)^(n-i), i, 0, (n-j))/(2*n-2*j)!), j, 0, n); /* _Vladimir Kruchinin, Jun 08 2011 */

CROSSREFS

Sequence in context: A318002 A323567 A304865 * A286928 A321042 A244820

Adjacent sequences:  A003706 A003707 A003708 * A003710 A003711 A003712

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

STATUS

approved

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Last modified February 24 07:19 EST 2020. Contains 332199 sequences. (Running on oeis4.)