%I A082141
%S A082141 1,8,72,480,2640,12672,54912,219648,823680,2928640,9957376,32587776,
%T A082141 103194624,317521920,952565760,2794192896,8033304576,22682271744,
%U A082141 63006310400,172438323200,465583472640,1241555927040,3273192898560
%N A082141 A transform of C(n,7).
%C A082141 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.
%F A082141 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).
%F A082141 ceil(binomial(n+7,7)*2^(n-1)). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 01 2006
%e A082141 a(0)=(2^(-1)+0^0/2)C(7,0)=2*(1/2)=1 (use 0^0=1)
%p A082141 [seq (ceil(binomial(n+7,7)*2^(n-1)),n=0..22)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 01 2006
%Y A082141 Cf. A082140, A082139, A054851.
%Y A082141 Sequence in context: A044576 A104453 A143945 this_sequence A054615 A111919 
               A052379
%Y A082141 Adjacent sequences: A082138 A082139 A082140 this_sequence A082142 A082143 
               A082144
%K A082141 easy,nonn
%O A082141 0,2
%A A082141 Paul Barry (pbarry(AT)wit.ie), Apr 06 2003