A237647 G.f. satisfies: A(x) = (1 + x + x^2)^7 * A(x^2)^4.

1, 7, 56, 273, 1463, 6048, 26537, 97903, 377384, 1281497, 4502463, 14322560, 46849089, 141332583, 436556440, 1259742225, 3710541975, 10308494560, 29165172617, 78396244591, 214217633672, 559335671353, 1482519853311, 3772127020032, 9731443674113, 24191903115079, 60918829766648

Offset: 0

Author

Paul D. Hanna, May 04 2014

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 7*x + 56*x^2 + 273*x^3 + 1463*x^4 + 6048*x^5 + 26537*x^6 +...
where:
A(x) = (1+x+x^2)^7 * (1+x^2+x^4)^28 * (1+x^4+x^8)^112 * (1+x^8+x^16)^448 * (1+x^16+x^32)^896 *...* (1 + x^(2^n) + x^(2*2^n))^(7*4^n) *...
		

Crossrefs

Cf. A237646, A237648, A237650.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,#binary(n),A=(1+x+x^2)^7*subst(A^4,x,x^2) +x*O(x^n));polcoeff(A,n)}
for(n=0,50,print1(a(n),", "))

PARI

{a(n)=local(A=1+x);A=prod(k=0,#binary(n),(1+x^(2^k)+x^(2*2^k)+x*O(x^n))^(7*4^k));polcoeff(A,n)}
for(n=0,50,print1(a(n),", "))

Formula

The odd-indexed bisection of A237646.

The 7th self-convolution of A237648.

G.f. A(x) satisfies:

(1) A(x) = Product_{n>=0} ( 1 + x^(2^n) + x^(2*2^n) )^(7*4^n).

(2) A(x) / A(-x) = (1+x+x^2)^7 / (1-x+x^2)^7.