The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360479

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A360479

Expansion of Sum_{k>=0} (x * (1 + (k * x)^2))^k.
(history; published version)

#40 by Vaclav Kotesovec at Sun Feb 19 10:55:25 EST 2023

STATUS

editing

approved

#39 by Vaclav Kotesovec at Sun Feb 19 10:54:40 EST 2023

CROSSREFS

Cf. A360592, A360747, A360699.

STATUS

approved

editing

#38 by Vaclav Kotesovec at Sun Feb 19 10:30:14 EST 2023

STATUS

editing

approved

#37 by Vaclav Kotesovec at Sun Feb 19 10:29:59 EST 2023

LINKS

Vaclav Kotesovec, <a href="/A360479/a360479.jpg">Graph - the asymptotic ratio (10000 terms)</a>

#36 by Vaclav Kotesovec at Sun Feb 19 10:29:17 EST 2023

FORMULA

a(n) ~ exp(exp(4/3)*n^(1/3)/3^(1/3)) * n^(2*n/3) / 3^(2*n/3 + 1) * (1 + (3^(1/3)/(8*exp(4/3)) - 13*exp(8/3)/(6*3^(2/3))) / n^(1/3) + (67/(128*3^(1/3)*exp(8/3)) - 5*3^(2/3)*exp(4/3)/16 + 169*exp(16/3)/(216*3^(1/3))) / n^(2/3) + (3929/2304 + 497/(1024*exp(4)) + 7913*exp(4)/1728 - 2197*exp(8)/11664)/n). - Vaclav Kotesovec, Feb 19 2023

STATUS

approved

editing

#35 by Vaclav Kotesovec at Sun Feb 19 10:08:55 EST 2023

STATUS

editing

approved

#34 by Vaclav Kotesovec at Sun Feb 19 10:08:50 EST 2023

LINKS

Vaclav Kotesovec, <a href="/A360479/b360479.txt">Table of n, a(n) for n = 0..635</a>

STATUS

approved

editing

#33 by Michael De Vlieger at Sun Feb 19 09:21:28 EST 2023

STATUS

proposed

approved

#32 by Joerg Arndt at Sun Feb 19 08:55:22 EST 2023

STATUS

editing

proposed

#31 by Vaclav Kotesovec at Sun Feb 19 08:54:51 EST 2023

MATHEMATICA

Join[{1}, Table[Sum[Binomial[n - 2*k, k] * (n - 2*k)^(2*k), {k, 0, n/3}], {n, 1, 30}]] (* Vaclav Kotesovec, Feb 19 2023 *)

STATUS

proposed

editing