A323490 Numerators of the sequence c(n) satisfying Sum_{k=0..n} c(k)/(n+k+1) = 0 with c(0)=1.

1, -3, 5, 77, 277, 140173, 1743859, 2076083, 259374867533, 57573296785133, 770098483166113, 5605884055023955789, 7228014618092706553, 3332173791979508526419, 27269879914911094298619533, 91854722122840672285969818121, 10712330835046717680588811970893, 283551664519128905300910019306673

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Alexander Kalmynin, Petr Kosenko, Orthorecursive expansion of unity, arXiv:1901.04044 [math.NT], 2019.

Example

The sequence c(n) begins: 1, -3/2, 5/24, 77/720, 277/4480, 140173/3628800, ...

Prog

(PARI) lista(nn) = {my(c0 = 1, vc = vector(nn)); for (n=1, nn, vc[n] = -(2*n+1)*(c0/(n+1) + sum(k=1, n-1, vc[k]/(n+k+1))); ); apply(x->numerator(x), concat([c0], vc)); }

Crossrefs

Cf. A323491 (denominators), A323492 (sign changes).

Sequence in context: A306255 A122912 A062214 * A368015 A144617 A301492

Adjacent sequences: A323487 A323488 A323489 * A323491 A323492 A323493

Keyword

sign,frac

Author

Michel Marcus, Jan 16 2019

Status

approved