A129357 G.f.: A(x) = Product_{n>=1} [ (1-x)^4*(1 + 4x + 10x^2 +...+ n(n+1)(n+2)/3!*x^(n-1)) ].

1, -4, -4, 36, -64, 256, -1328, 4488, -11406, 17700, 14716, -194508, 662768, -1374476, 2210780, -5820284, 25965483, -95963664, 259794360, -545959440, 952758316, -1278120568, 60070208, 8030404744, -34554134770, 94549651780, -196087124052, 330754522268, -511020392180

Offset: 0

Author

Paul D. Hanna, Apr 11 2007

Keywords

• sign

Examples

			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)*...
Terms are divisible by 4 except at positions given by:
a(n) == 1 (mod 4) at n = 16*[0, 2, 5, 15, 22, 26, 40,...];
a(n) == -1 (mod 4) at n = 16*[1, 7, 12, 35, 51, 57,...];
a(n) == 2 (mod 4) at n = 8*[1,3,5,6,8,9,13,15,16,19,..,A129359(k),..].
		

Crossrefs

Cf. A129355, A129356, A129358, A129359.

Programs

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))}

Formula

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) ].