A107350 - OEIS

%I #20 Mar 10 2023 05:39:16

%S 1,4,34,346,3965,48396,615966,8082457,108545916,1484716135,

%T 20612084010,289688970195,4113620233260,58930127470164,

%U 850641610106596,12360278974175769,180648953113093368,2653875476976308643,39167191622334514398,580439539153823110678,8633956582855204662785

%N Number of isogons with a certain property.

%C This and A060005 appear in the reference as incidental sequences when computing A007219.

%H Seiichi Manyama, <a href="/A107350/b107350.txt">Table of n, a(n) for n = 1..200</a>

%H L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, <a href="http://www.jstor.org/stable/2690648">Serial isogons of 90 degrees</a>, Math. Mag. 64 (1991), 315-324.

%F product[ {1+x^(2i+1)},i=0,1,...,4n-1] = 1+...+2*a(n)*x^(8n^2)+.... (g.f.). - _R. J. Mathar_, May 08 2007

%F a(n) = A292476(2*n)/2. - _Seiichi Manyama_, Sep 18 2017

%p A107350 := proc(n) res := 1 ; for i from 0 to 4*n-1 do res := taylor(res*(1+x^(2*i+1)),x=0,8*n^2+1) ; od ; coeftayl(res,x=0,8*n^2)/2 ; end: for n from 1 to 25 do printf("%d, ",A107350(n)) ; od ; # _R. J. Mathar_, May 08 2007

%t a[n_] := SeriesCoefficient[Product[x^(2k - 1) + 1/x^(2k - 1), {k, 1, 4n}], {x, 0, 0}]/2;

%t Table[a[n], {n, 1, 25}] (* _Jean-François Alcover_, Mar 10 2023 *)

%Y Cf. A007219, A060005, A292476.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, May 23 2005

%E More terms from _R. J. Mathar_, May 08 2007