Search: id:A082140
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%I A082140
%S A082140 1,7,56,336,1680,7392,29568,109824,384384,1281280,4100096,12673024,
%T A082140 38019072,111132672,317521920,889061376,2444918784,6615662592,
%U A082140 17641766912,46425702400,120706826240,310388981760,790081044480
%N A082140 A transform of C(n,6).
%C A082140 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.
%F A082140 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).
%F A082140 ceil(binomial(n+6,6)*2^(n-1)). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 01 2006
%e A082140 a(0)=(2^(-1)+0^0/2)C(6,0)=2*(1/2)=1 (use 0^0=1)
%p A082140 [seq (ceil(binomial(n+6,6)*2^(n-1)),n=0..22)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 01 2006
%Y A082140 Cf. A082139, A080951.
%Y A082140 For n>0, a(n) = 1/2 * A002409(n).
%Y A082140 Sequence in context: A090224 A047664 A055345 this_sequence A054614 A104896 
               A122996
%Y A082140 Adjacent sequences: A082137 A082138 A082139 this_sequence A082141 A082142 
               A082143
%K A082140 easy,nonn
%O A082140 0,2
%A A082140 Paul Barry (pbarry(AT)wit.ie), Apr 06 2003

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