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A002017
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E.g.f. exp(sin(x)).
(Formerly M2709 N1086)
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9
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1, 1, 1, 0, -3, -8, -3, 56, 217, 64, -2951, -12672, 5973, 309376, 1237173, -2917888, -52635599, -163782656, 1126610929, 12716052480, 20058390573, -495644917760, -3920482183827, 4004259037184, 256734635981833, 1359174582304768
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Number of set partitions of 1..n into odd parts with an even number of parts of size == 3 (mod 4), minus the number of such partitions with an odd number of parts of size == 3 (mod 4). [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 29 2010]
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REFERENCES
| E. T. Bell, Exponential numbers, Amer. Math. Monthly, 41 (1934), 411-419.
CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.
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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
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FORMULA
| a(n)=2*sum(j=0..(n-1)/2, (sum(i=0..(n-2*j)/2, (2*i-n+2*j)^n*binomial(n-2*j,i)*(-1)^(n-j-i)))/(2^(n-2*j)*(n-2*j)!)), n>0, a(0)=1. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Jun 10 2011]
a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator sqrt(1-x^2)*d/dx. Cf. A003724. - Peter Bala, Dec 06 2011
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EXAMPLE
| For n=6, there are 6 partitions with part sizes [5,1], 10 with sizes [3^2], 20 with sizes [3,1^3], and 1 with sizes [1^6]; 6 + 10 - 20 + 1 = -3. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 29 2010]
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PROG
| (Maxima) a(n):=2*sum((sum((2*i-n+2*j)^n*binomial(n-2*j, i)*(-1)^(n-j-i), i, 0, (n-2*j)/2))/(2^(n-2*j)*(n-2*j)!), j, 0, (n-1)/2); [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Jun 10 2011]
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CROSSREFS
| a(2n) = A007301(n), |a(2n+1)| = |A003722(n)|.
Cf. A003724. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Apr 29 2010]
Sequence in context: A146975 A046970 A058936 * A118582 A086179 A185453
Adjacent sequences: A002014 A002015 A002016 * A002018 A002019 A002020
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KEYWORD
| sign,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Extended with signs 10/98 by Christian G. Bower (bowerc(AT)usa.net).
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