%I A082138
%S A082138 1,4,20,80,280,896,2688,7680,21120,56320,146432,372736,931840,2293760,
%T A082138 5570560,13369344,31752192,74711040,174325760,403701760,928514048,
%U A082138 2122317824,4823449600,10905190400,24536678400,54962159616,122607894528
%N A082138 A transform of C(n,3).
%C A082138 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.
%F A082138 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).
%F A082138 ceil(binomial(n+3,3)*2^(n-1)). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 01 2006
%e A082138 a(0)=(2^(-1)+0^0/2)C(3,0)=2*(1/2)=1 (use 0^0=1)
%p A082138 [seq (ceil(binomial(n+3,3)*2^(n-1)),n=0..26)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 01 2006
%Y A082138 Cf. A080929, A082139.
%Y A082138 Cf. A082140, A082141, A082139, A080951, A080929, A057711.
%Y A082138 Sequence in context: A121257 A145563 A125669 this_sequence A074358 A055296 
               A140532
%Y A082138 Adjacent sequences: A082135 A082136 A082137 this_sequence A082139 A082140 
               A082141
%K A082138 easy,nonn
%O A082138 0,2
%A A082138 Paul Barry (pbarry(AT)wit.ie), Apr 06 2003