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A082140
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A transform of C(n,6).
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10
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1, 7, 56, 336, 1680, 7392, 29568, 109824, 384384, 1281280, 4100096, 12673024, 38019072, 111132672, 317521920, 889061376, 2444918784, 6615662592, 17641766912, 46425702400, 120706826240, 310388981760, 790081044480
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Seventh row of number array A082137. C(n,6) has e.g.f. (x^6/6!)exp(x). The transform averages the binomial and inverse binomial transforms.
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FORMULA
| a(n)=(2^(n-1)+0^n/2)C(n+6, n)= sum{j=0..n, C(n+6, j+6)C(j+6, 6)(1+(-1)^j)/2 } G.f.: (1-7x+42x^2-140x^3+280x^4-336x^5+224x^6-64x^7)/(1-2x)^7 E.g.f. (x^6/6!)exp(x)cosh(x) (with 6 leading zeros).
ceil(binomial(n+6,6)*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(6,0)=2*(1/2)=1 (use 0^0=1)
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MAPLE
| [seq (ceil(binomial(n+6, 6)*2^(n-1)), n=0..22)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 01 2006
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CROSSREFS
| Cf. A082139, A080951.
For n>0, a(n) = 1/2 * A002409(n).
Sequence in context: A047664 A055345 A180287 * A054614 A104896 A122996
Adjacent sequences: A082137 A082138 A082139 * A082141 A082142 A082143
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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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