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A082138
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A transform of C(n,3).
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9
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1, 4, 20, 80, 280, 896, 2688, 7680, 21120, 56320, 146432, 372736, 931840, 2293760, 5570560, 13369344, 31752192, 74711040, 174325760, 403701760, 928514048, 2122317824, 4823449600, 10905190400, 24536678400, 54962159616, 122607894528
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fourth row of number array A082137. C(n,3) has e.g.f. (x^3/3!)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+3, n)=sum{j=0..n, C(n+3, j+3)C(j+3, 3)(1+(-1)^j)/2 } G.f.: (1-4x+12x^2-16x^3+8x^4)/(1-2x)^4 E.g.f. (x^3/3!)exp(x)cosh(x) (preceded by 3 zeros).
ceil(binomial(n+3,3)*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(3,0)=2*(1/2)=1 (use 0^0=1)
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MAPLE
| [seq (ceil(binomial(n+3, 3)*2^(n-1)), n=0..26)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 01 2006
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PROG
| (MAGMA) [(Ceiling(Binomial(n+3, 3)*2^(n-1))) : n in [0..30]]; // Vincenzo Librandi, Sep 22 2011
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CROSSREFS
| Cf. A080929, A082139.
Cf. A082140, A082141, A082139, A080951, A080929, A057711.
Sequence in context: A121257 A145563 A125669 * A074358 A055296 A140532
Adjacent sequences: A082135 A082136 A082137 * A082139 A082140 A082141
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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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