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A082139
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A transform of C(n,5).
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11
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1, 6, 42, 224, 1008, 4032, 14784, 50688, 164736, 512512, 1537536, 4472832, 12673024, 35094528, 95256576, 254017536, 666796032, 1725825024, 4410441728, 11142168576, 27855421440, 68975329280, 169303080960, 412216197120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sixth row of number array A082137. C(n,5) has e.g.f. (x^5/5!)exp(x). The transform averages the binomial and inverse binomial transforms.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
| a(n)=(2^(n-1)+0^n/2)C(n+5, n)=sum{j=0..n, C(n+5, j+5)C(j+5, 5)(1+(-1)^j)/2 } G.f.: (1-6x+30x^2-80x^3+120x^4-96x^5+32x^6)/(1-2x)^6 E.g.f. (x^5/5!)exp(x)cosh(x) (preceded by 5 zeros).
ceil(binomial(n+5,5)*2^(n-1)). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 01 2006
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EXAMPLE
| a(0)=(2^(-1)+0^0/2)C(5,0)=2*(1/2)=1 (use 0^0=1)
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MAPLE
| [seq (ceil(binomial(n+5, 5)*2^(n-1)), n=0..23)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 01 2006
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PROG
| (MAGMA) [(Ceiling(Binomial(n+5, 5)*2^(n-1))) : n in [0..30]]; // Vincenzo Librandi, Sep 22 2011
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CROSSREFS
| Cf. A080951, A082138.
Equals 2 * A080952.
Cf. A082140, A082141, A082138, A080951, A080929, A057711.
Sequence in context: A062136 A047663 A054642 * A180286 A054613 A141834
Adjacent sequences: A082136 A082137 A082138 * A082140 A082141 A082142
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 06 2003
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