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A082141
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A transform of C(n,7).
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9
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1, 8, 72, 480, 2640, 12672, 54912, 219648, 823680, 2928640, 9957376, 32587776, 103194624, 317521920, 952565760, 2794192896, 8033304576, 22682271744, 63006310400, 172438323200, 465583472640, 1241555927040, 3273192898560
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Eighth row of number array A082137. C(n,7) has e.g.f. (x^7/7!)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+7, n)=sum{j=0..n, C(n+7, j+7)C(j+7, 7)(1+(-1)^j)/2 } G.f.: (1-8x+56x^2-224x^3+560x^4-896x^5+896x^6-512x^7+128x^8)/(1-2x)^8 E.g.f. (x^7/7!)exp(x)cosh(x) (with 7 leading zeros).
ceil(binomial(n+7,7)*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(7,0)=2*(1/2)=1 (use 0^0=1)
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MAPLE
| [seq (ceil(binomial(n+7, 7)*2^(n-1)), n=0..22)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 01 2006
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CROSSREFS
| Cf. A082140, A082139, A054851.
Sequence in context: A143945 A189954 A180288 * A054615 A111919 A052379
Adjacent sequences: A082138 A082139 A082140 * A082142 A082143 A082144
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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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