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A132912
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a(n)=C(n+2,2)(2n)!/2^n.
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1
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1, 3, 36, 900, 37800, 2381400, 209563200, 24518894400, 3677834160000, 687754987920000, 156808137245760000, 42808621468092480000, 13784376112725778560000, 5169141042272166960000000, 2233068930261576126720000000, 1100902982618957030472960000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Define T(n,k)=((1+(-1)^n)/2)*C(k-1+n/2, n/2)*n!/2^(n/2). Then T(n,k) has e.g.f. 1/sum{j=0..k, C(k,j)*(-1)^j*x^(2j)/2^j}. T(n,1) is A000680 with interpolated zeros. T(n,2) is A132911.
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FORMULA
| E.g.f.: 1/(1-(3/2)x^2+(3/4)x^4-(1/8)x^6) (with interpolated zeros);
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MATHEMATICA
| Table[(Binomial[n+2, 2](2n)!)/2^n, {n, 0, 20}] (* From Harvey P. Dale, Sep 18 2011 *)
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CROSSREFS
| Sequence in context: A122220 A186730 A004824 * A126447 A102921 A193302
Adjacent sequences: A132909 A132910 A132911 * A132913 A132914 A132915
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 04 2007
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EXTENSIONS
| More terms from Harvey P. Dale, Sep 18 2011
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