A373196 Maximal coefficient (in absolute value) in the numerator of C({1..n},x).

1, 1, 2, 17, 444, 66559954, 14648786369948422, 791540878703169050660325841979096789557779, 1918013047695258943191946313451491492494186620117241479813740479213857275772347178176158

Offset

0,3

Links

Table of n, a(n) for n=0..8.

Formula

C({s},x) = Sum_{i in {s}} (C({s}-{i},x)*x^i)/(1 - Sum_{i in {s}} (x^i)) with C({},x) = 1.

Example

C_x({1,2,3},x) = (-x^15 - 5*x^14 - 12*x^13 - 17*x^12 - 11*x^11 + 4*x^10 + 16*x^9 + 10*x^8 - 6*x^6)/(x^15 + 4*x^14 + 7*x^13 + 4*x^12 - 8*x^11 - 18*x^10 - 13*x^9 + 7*x^8 + 19*x^7 + 11*x^6 - 6*x^5 - 10*x^4 - 2*x^3 + 3*x^2 + 2*x - 1) with maximal coefficient abs(-17) in the numerator, so a(3) = 17.

Prog

(PARI)
C_x(s)={my(g=if(#s <1, 1, sum(i=1, #s, C_x(s[^i])*x^(s[i]))/(1-sum(i=1, #s, x^(s[i]))))); return(g)}
a(n)={vecmax(abs(Vec(numerator(C_x([1..n])))))}

Crossrefs

Cf. A107429, A114536, A278567.

Sequence in context: A015202 A308864 A370704 * A217284 A220476 A293178

Adjacent sequences: A373193 A373194 A373195 * A373197 A373198 A373199

Keyword

nonn

Author

John Tyler Rascoe, Jun 28 2024

Status

approved