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%I #3 Mar 30 2012 18:37:03
%S 1,-4,-4,36,-64,256,-1328,4488,-11406,17700,14716,-194508,662768,
%T -1374476,2210780,-5820284,25965483,-95963664,259794360,-545959440,
%U 952758316,-1278120568,60070208,8030404744,-34554134770,94549651780,-196087124052,330754522268,-511020392180
%N G.f.: A(x) = Product_{n>=1} [ (1-x)^4*(1 + 4x + 10x^2 +...+ n(n+1)(n+2)/3!*x^(n-1)) ].
%F G.f.: A(x) = Product_{n>=1} [ 1 - (n+1)(n+2)(n+3)/3!*x^n + 3n(n+2)(n+3)/3!*x^(n+1) - 3n(n+1)(n+3)/3!*x^(n+2) + n(n+1)(n+2)/3!*x^(n+3) ].
%e G.f.: A(x) = (1-4x+6x^2-4x^3+x^4)*(1-10x^2+20x^3-15x^4+4x^5)*(1-20x^3+45x^4-36x^5+10x^6)*(1-35x^4+84x^5-70x^6+20x^7)*...
%e Terms are divisible by 4 except at positions given by:
%e a(n) == 1 (mod 4) at n = 16*[0, 2, 5, 15, 22, 26, 40,...];
%e a(n) == -1 (mod 4) at n = 16*[1, 7, 12, 35, 51, 57,...];
%e a(n) == 2 (mod 4) at n = 8*[1,3,5,6,8,9,13,15,16,19,..,A129359(k),..].
%o (PARI) {a(n)=if(n==0,1,polcoeff(prod(k=1,n,(1-x)^4*sum(j=1,k,binomial(j+2,3)*x^(j-1)) +x*O(x^n)),n))}
%Y Cf. A129355, A129356, A129358, A129359.
%K sign
%O 0,2
%A _Paul D. Hanna_, Apr 11 2007
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