A357557 a(n) is the numerator of the coefficient c in the polynomial of the form y(x)=x^n+c such that starting with y(x)=x for n=1 each polynomial is C-1 continuous with the previous one.

0, 1, 43, 3481, 12647597, 380547619, 340607106994117, 23867104301800579837, 13408353860832026243555117, 43926321999197203038889578577, 13055436009603783636664151666161626100547, 6766346844526064783736339920897644104961

Offset

1,3

Comments

The polynomials y(x)=x^n+c(n) can only be connected at x=n/(n+1) and with coefficients c(n) = { 0, 1/4, 43/108, 3481/6912, ... }. The denominator of c(n) is A061464. The numerator is our sequence a(n)

Links

Inigo Quilez, Table of n, a(n) for n = 1..50

Inigo Quilez, Live demo of the polynomials y(x)

Formula

a(n) = numerator of Sum_{i=1..n} (i^i)/((i+1)^(i+1)).

Prog

(PARI) a(n) = my(p=1); numerator(sum(i=2, n, p/(p=i^i))); \\ Kevin Ryde, Oct 03 2022

Crossrefs

Cf. A061464 (denominators).

Sequence in context: A130014 A246535 A265234 * A015323 A145315 A110704

Adjacent sequences: A357554 A357555 A357556 * A357558 A357559 A357560

Keyword

nonn,frac

Author

Inigo Quilez, Oct 03 2022

Status

approved