A215201 Central coefficients in Product_{k=0..n-1} (1 + 2^k*x + x^2).

1, 1, 4, 22, 210, 3690, 123928, 8128636, 1053430654, 271360277914, 139369979870592, 142937572590524820, 292964593467450613956, 1200451226250888081523716, 9836015215866134276407221456, 161168995194103116779231535612216, 5281443249372612678523678805252800566

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) ~ c * 2^(n*(n-1)/2), where c = 3.97351011200975226288353040315941996... . - Vaclav Kotesovec, Feb 10 2015

Example

The coefficients in Product_{k=0..n-1} (1+2^k*x+x^2), n>=0, form the triangle:
1;
1, 1, 1;
1, 3, 4, 3, 1;
1, 7, 17, 22, 17, 7, 1;
1, 15, 74, 165, 210, 165, 74, 15, 1;
1, 31, 315, 1364, 2924, 3690, 2924, 1364, 315, 31, 1;
1, 63, 1308, 11475, 46887, 98622, 123928, 98622, 46887, 11475, 1308, 63, 1; ...
in which the central terms of the rows form this sequence.

Mathematica

Flatten[{1, Table[Coefficient[Expand[Product[1 + 2^k*x + x^2, {k, 0, n-1}]], x^n], {n, 1, 20}]}] (* Vaclav Kotesovec, Feb 10 2015 *)

Prog

(PARI) {a(n)=polcoeff(prod(k=0, n-1, 1+2^k*x+x^2+x*O(x^n)), n)}
for(n=0, 21, print1(a(n), ", "))

Crossrefs

Sequence in context: A303330 A280828 A103437 * A063380 A113385 A356285

Adjacent sequences: A215198 A215199 A215200 * A215202 A215203 A215204

Keyword

nonn

Author

Paul D. Hanna, Aug 05 2012

Status

approved