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Euler transform is sequence A004016.
1

%I #5 Apr 30 2014 01:36:11

%S 6,-21,76,-345,1734,-8906,46662,-250257,1365388,-7538421,42030150,

%T -236312690,1338000774,-7620721077,43626920908,-250869973089,

%U 1448248263558,-8389624496618,48751103123142,-284073748405401,1659452645344972,-9715933503018165

%N Euler transform is sequence A004016.

%F a(q) = Prod_{k>0} (1 - q^k)^-a(k).

%o (PARI) {a(n) = local(A, S); if( n<1, 0, A = 1 + x * O(x^n); S = sum( k= 1, n, 6 * sumdiv( k, d, kronecker( d, 3)) * x^k, A); for( k = 1, n-1, S *= (A - x^k) ^ polcoeff( S, k)); polcoeff( S, n))}

%Y Cf. A004016.

%K sign

%O 1,1

%A _Michael Somos_, Jul 08 2011