A260952 - OEIS

%I #9 Mar 07 2022 06:14:26

%S 1,-1,-1,-5,-35,-319,-3557,-46617,-699547,-11801263,-220778973,

%T -4532376577,-101246459811,-2444155497191,-63397685488165,

%U -1758278168174137,-51920205021872395,-1626358286062507551,-53865503179448478605,-1880864793407486366353

%N Coefficients in asymptotic expansion of the sequences A109253 and A112225.

%C The values 1,5,35,319,... also are the number of Feynman diagrams of the Green's function of 2,4,6,8,... vertices which have no tadpoles (i.e. no edges that connect a vertex to itself), a subset of the graphs in A000698, vixra:1901.0148. This is likely a random coincidence. - _R. J. Mathar_, Mar 07 2022

%H Vaclav Kotesovec, <a href="/A260952/b260952.txt">Table of n, a(n) for n = 0..124</a>

%F A109253(n)/(n!*2^n) ~ Sum_{k>=0} a(k)/(2*n)^k.

%F A112225(n)/(n!*2^(n-1)) ~ Sum_{k>=0} a(k)/(2*n)^k.

%F Conjecture: a(k) ~ -k! * 2^(k+1) / (9 * (log(3))^(k+1)).

%e A109253(n)/(n!*2^n) ~ (1 - 1/(2*n) - 1/(4*n^2) - 5/(8*n^3) - 35/(16*n^4) - ...

%e A112225(n)/(n!*2^(n-1)) ~ (1 - 1/(2*n) - 1/(4*n^2) - 5/(8*n^3) - 35/(16*n^4) - ...

%Y Cf. A109253, A112225.

%K sign

%O 0,4

%A _Vaclav Kotesovec_, Aug 05 2015