cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Billy Bolton

Billy Bolton's wiki page.

Billy Bolton has authored 2 sequences.

A362407 Numerators of the expansion of the series reversion of sin(x) + x, odd powers only.

Original entry on oeis.org

1, 1, 1, 43, 223, 60623, 764783, 107351407, 2499928867, 596767688063, 22200786516383, 64470807442488761, 3504534741776035061, 3597207408242668198973, 268918457620309807441853, 185388032403184965693274807, 18241991360742724891839902347
Offset: 0

Views

Author

Billy Bolton, Apr 18 2023

Keywords

Examples

			f^-1(x) = (1/2)*x + (1/96)*x^3 + (1/1920)*x^5 + (43/1290240)*x^7 + ...

Crossrefs

Cf. A362406 (denominators).
Cf. A302977, A306254.

Programs

  • PARI
    a(n) = numerator(polcoef(serreverse(sin(x + O(x^(2*n))) + x), 2*n-1)) \\ Andrew Howroyd, Apr 18 2023

Formula

Conjecture: a(n) = abs(A302977(n)).

A362406 Denominators of the expansion of the series reversion of sin(x) + x, odd powers only.

Original entry on oeis.org

2, 96, 1920, 1290240, 92897280, 326998425600, 51011754393600, 85699747381248000, 23310331287699456000, 63777066403145711616000, 26786367889321198878720000, 867449737727777704488468480000, 520469842636666622693081088000000, 5845917272495039506088686780416000000
Offset: 0

Views

Author

Billy Bolton, Apr 18 2023

Keywords

Examples

			f^-1(x) = (1/2)*x + (1/96)*x^3 + (1/1920)*x^5 + (43/1290240)*x^7 + ...

Crossrefs

Cf. A362407 (numerators).
Cf. A302977, A306254.

Programs

  • PARI
    a(n) = denominator(polcoef(serreverse(sin(x + O(x^(2*n))) + x), 2*n-1)) \\ Andrew Howroyd, Apr 18 2023

Formula

Conjecture: a(n) = 2*A306254(n)/(4^(n+1)).

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