A219931 -id:A219931 - cp's OEIS frontend

A239739 a(n) = n4^(2n+1).

0, 64, 2048, 49152, 1048576, 20971520, 402653184, 7516192768, 137438953472, 2473901162496, 43980465111040, 774056185954304, 13510798882111488, 234187180623265792, 4035225266123964416, 69175290276410818560, 1180591620717411303424, 20070057552195992158208

Offset: 0

Peter Luschny, Mar 26 2014

Appears in asymptotic expansions of the logarithm of the central binomial and the Catalan numbers. (See Kessler and Schiff, page 2.)

Vincenzo Librandi, Table of n, a(n) for n = 0..200
D. Kessler and J. Schiff, The asymptotics of factorials, binomial coefficients and Catalan numbers. April 2006.
Index entries for linear recurrences with constant coefficients, signature (32,-256).

Cf. A219931, A220002, A220422, A267796, A013709.

[n*4^(2*n+1): n in [0..25]]; // Vincenzo Librandi, Apr 25 2014

CoefficientList[Series[64 x /(1 - 16 x)^2, {x, 0, 20}], x] (* Vincenzo Librandi, Apr 25 2014 *)
LinearRecurrence[{32,-256},{0,64},20] (* Harvey P. Dale, May 06 2021 *)

G.f.: 64*x / (1 - 16*x)^2. [Bruno Berselli, Mar 26 2014]
(n-1)*a(n) - 16*n*a(n-1) = 0. [Bruno Berselli, Mar 26 2014]
a(n) = n*A013709(n). - Michel Marcus, Jan 30 2016

A385054 Numbers k such that (2k-1)2^valuation(k, 2) != denominator(2Euler(2k-1, 1)/(2*k-1)).

Original entry on oeis.org

60, 140, 196, 280, 295, 332, 390, 468, 574, 581, 604, 605, 621, 740, 760, 826, 876, 935, 1012, 1070, 1148, 1183, 1185, 1210, 1225, 1240, 1269, 1278, 1284, 1376, 1420, 1484, 1526, 1535, 1556, 1690, 1692, 1715, 1828, 1906, 1908, 1910, 1914, 1928, 1935, 1964, 2000

Offset: 1

Peter Luschny, Jun 16 2025

nonn

Cf. A219931.

a := n -> ifelse((2*n-1)*2^ordp(n,2) = denom(2*euler(2*n-1,1)/(2*n-1)), NULL, n):
seq(a(n), n = 1..1000);

Select[Range[1000], Denominator[2*EulerE[2*# - 1, 1]/(2*# - 1)] != (2*# - 1)*2^IntegerExponent[#, 2] &] (* Amiram Eldar, Jun 16 2025 *)

cp's OEIS Frontend

A239739 a(n) = n4^(2n+1).

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A385054 Numbers k such that (2k-1)2^valuation(k, 2) != denominator(2Euler(2k-1, 1)/(2*k-1)).

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cp's OEIS Frontend

A239739 a(n) = n*4^(2*n+1).

Views

Author

Keywords

Comments

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Crossrefs

Programs

Magma

Mathematica

Formula

A385054 Numbers k such that (2*k-1)*2^valuation(k, 2) != denominator(2*Euler(2*k-1, 1)/(2*k-1)).

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Maple

Mathematica

A239739 a(n) = n4^(2n+1).

A385054 Numbers k such that (2k-1)2^valuation(k, 2) != denominator(2Euler(2k-1, 1)/(2*k-1)).