A129355 G.f.: A(x) = Product_{n>=1} [ (1-x)^2*(1 + 2x + 3x^2 +...+ n*x^(n-1)) ].

1, -2, -2, 4, -1, 12, -26, 38, -51, 6, 98, -190, 138, 60, 132, -1296, 2990, -3738, 3350, -3752, 4077, 1194, -12272, 18528, -14848, 9018, -2002, 5644, -86729, 290596, -514158, 611070, -603150, 657792, -952808, 1406568, -1208636, -635286, 3507362, -5062866, 3791614

Offset

0,2

Comments

a(k) == 1 (mod 2) at k = 4*A001318(n) for n>=0, where A001318 are the generalized pentagonal numbers: m(3m-1)/2, m=0,+-1,+-2,....

Links

Table of n, a(n) for n=0..40.

Formula

G.f.: A(x) = Product_{n>=1} ( 1 - (n+1)*x^n + n*x^(n+1) ) . G.f.: A(x) = Product_{n>=1} [ (1-x)*(1 + x + x^2 +...+ x^(n-1) - n*x^n) ] .

Example

A(x) = (1 - 2x + x^2)(1 - 3x^2 + 2x^3)(1 - 4x^3 + 3x^4)(1 - 5x^4 + 4x^5)*...
Terms are even except at positions given by:
a(n) == 1 (mod 2) at n = [0, 4, 8, 20, 28, 48, 60, 88,...,4*A001318(n),...].

Prog

(PARI) a(n)=if(n==0, 1, polcoeff(prod(k=1, n, 1-(k+1)*x^k+k*x^(k+1)+x*O(x^n)), n))

Crossrefs

Cf. A129356, A129357, A129358.

Sequence in context: A243548 A105478 A114427 * A080963 A133692 A033715

Adjacent sequences: A129352 A129353 A129354 * A129356 A129357 A129358

Keyword

sign

Author

Paul D. Hanna, Apr 10 2007

Status

approved