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

Author

Inigo Quilez, Oct 03 2022

Keywords

• nonn
• frac

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)

Crossrefs

Cf. A061464 (denominators).

Programs

PARI

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

Formula

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