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Coefficients in an asymptotic expansion of sequence A002893.
2

%I #12 Nov 11 2016 03:42:53

%S 1,-1,1,2,7,59,616,6992,90847,1352549,22591681,417527582,8465505412,

%T 186906393764,4463901355096,114672825810272,3153127461349327,

%U 92405864554182329,2875362251645606611,94680648376734042062,3289274269898822961967,120235993277078434540619

%N Coefficients in an asymptotic expansion of sequence A002893.

%H Vaclav Kotesovec, <a href="/A274600/b274600.txt">Table of n, a(n) for n = 0..80</a>

%H Mathematics.StackExchange, <a href="http://math.stackexchange.com/questions/2006632/sum-involving-the-product-of-binomial-coefficients">sum involving the product of binomial coefficients</a>, Nov 10 2016.

%F Conjecture: a(n) ~ (2/log(3))^n * (n-1)! / (Pi*sqrt(3)).

%e A002893(n) ~ 3^(2*n+3/2)/(4*Pi*n) * (1 - 1/(4*n) + 1/(4*n)^2 + 2/(4*n)^3 + 7/(4*n)^4 + 59/(4*n)^5 + ...)

%Y Cf. A002893.

%K sign

%O 0,4

%A _Vaclav Kotesovec_, Nov 10 2016