|
| |
|
|
A132317
|
|
a(n) = [x^(2^n)] Product_{i=0..n} (1 + x^(2^i) )^(2^(n-i)); equals column 1 of triangle A132318.
|
|
2
|
| |
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Next term, a(8), has 126 digits.
|
|
|
LINKS
|
Table of n, a(n) for n=0..7.
|
|
|
EXAMPLE
|
a(0) = [x] (1+x) = 1;
a(1) = [x^2] (1+x)^2*(1+x^2) = 2;
a(2) = [x^4] (1+x)^4*(1+x^2)^2*(1+x^4) = 15;
a(3) = [x^8] (1+x)^8*(1+x^2)^4*(1+x^4)^2*(1+x^8) = 1024;
a(4) = [x^16] (1+x)^16*(1+x^2)^8*(1+x^4)^4*(1+x^8)^2*(1+x^16) = 7048181.
|
|
|
MATHEMATICA
|
Table[SeriesCoefficient[Product[(1 + x^(2^j))^(2^(n-j)), {j, 0, n}], {x, 0, 2^n}], {n, 0, 10}] (* Vaclav Kotesovec, Oct 09 2020 *)
|
|
|
PROG
|
(PARI) {a(n)=polcoeff(prod(i=0, n, (1 + x^(2^i) +x*O(x^(2^n)))^(2^(n-i))), 2^n)}
|
|
|
CROSSREFS
|
Cf. A132318, A132316.
Sequence in context: A007542 A090604 A007467 * A068409 A096232 A193869
Adjacent sequences: A132314 A132315 A132316 * A132318 A132319 A132320
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Paul D. Hanna, Aug 19 2007
|
|
|
STATUS
|
approved
|
| |
|
|
