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A143962 Binomial transform of A066247 (characteristic function of composite numbers).

%I A143962 #13 Jan 11 2023 11:44:46
%S A143962 0,0,0,0,1,5,16,42,99,220,476,1023,2201,4732,10102,21284,44103,89845,
%T A143962 180354,358226,707561,1396560,2764906,5501807,11005363,22101301,
%U A143962 44470622,89475559,179753753,360325116,720748862,1439561539,2873846383,5740501232,11484167472
%N A143962 Binomial transform of A066247 (characteristic function of composite numbers).
%H A143962 Alois P. Heinz, <a href="/A143962/b143962.txt">Table of n, a(n) for n = 0..1000</a>
%H A143962 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A143962 a(n) = Sum_{k=4..n} C(n,k)*A066247(k).
%e A143962 a(7) = [35,21,7,1]*[1,0,1,0] = 35+7 = 42.
%p A143962 a:= proc(n) local k,s; s:=0; for k from 4 to n do if not isprime(k) then s:= s+ binomial(n,k) fi od; s; end: seq (a(n), n=0..40);
%t A143962 a[n_] := Module[{k, s = 0}, For[k = 4, k <= n, k++, If[!PrimeQ[k], s = s + Binomial[n, k]]]; s]; Table [a[n], {n, 0, 40}] // Flatten (* _Jean-François Alcover_, Dec 30 2013, translated from Maple *)
%Y A143962 Cf. A007318, A066247.
%K A143962 nonn
%O A143962 0,6
%A A143962 _Alois P. Heinz_, Sep 05 2008