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%I #18 Nov 03 2023 06:42:58
%S 1,1,8,48,344,2460,18152,134512,1012664,7635987,58199208,443658688,
%T 3409213016,26184550496,202384723528,1562970918720,12133130451576,
%U 94094281551304,732910480638272,5702603044247504,44538031693977544
%N Central octonomial coefficients: largest coefficient of (1+x+...+x^7)^n.
%C Generally, largest coefficient of (1+x+...+x^k)^n is asymptotic to (k+1)^n * sqrt(6/(k*(k+2)*Pi*n)). - _Vaclav Kotesovec_, Aug 09 2013
%H Vaclav Kotesovec, <a href="/A025013/b025013.txt">Table of n, a(n) for n = 0..500</a> (first 200 terms from T. D. Noe)
%H Vaclav Kotesovec, <a href="/A025013/a025013.txt">Recurrence</a>.
%F a(n) ~ 8^n * sqrt(2/(21*Pi*n)). - _Vaclav Kotesovec_, Aug 09 2013
%t Flatten[{1,Table[Coefficient[Expand[Sum[x^j,{j,0,7}]^n],x^Floor[7*n/2]],{n,1,20}]}] (* _Vaclav Kotesovec_, Aug 09 2013 *)
%Y Cf. A001405, A002426, A005190, A005191, A018901, A025012, A025014.
%K easy,nonn
%O 0,3
%A _David W. Wilson_
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