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%I A357557 #24 Oct 18 2022 13:33:12
%S A357557 0,1,43,3481,12647597,380547619,340607106994117,23867104301800579837,
%T A357557 13408353860832026243555117,43926321999197203038889578577,
%U A357557 13055436009603783636664151666161626100547,6766346844526064783736339920897644104961
%N 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.
%C A357557 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)
%H A357557 Inigo Quilez, <a href="/A357557/b357557.txt">Table of n, a(n) for n = 1..50</a>
%H A357557 Inigo Quilez, <a href="https://www.shadertoy.com/view/sltfRs">Live demo of the polynomials y(x)</a>
%F A357557 a(n) = numerator of Sum_{i=1..n} (i^i)/((i+1)^(i+1)).
%o A357557 (PARI) a(n) = my(p=1); numerator(sum(i=2,n, p/(p=i^i))); \\ _Kevin Ryde_, Oct 03 2022
%Y A357557 Cf. A061464 (denominators).
%K A357557 nonn,frac
%O A357557 1,3
%A A357557 _Inigo Quilez_, Oct 03 2022

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