A260952 Coefficients in asymptotic expansion of the sequences A109253 and A112225.

1, -1, -1, -5, -35, -319, -3557, -46617, -699547, -11801263, -220778973, -4532376577, -101246459811, -2444155497191, -63397685488165, -1758278168174137, -51920205021872395, -1626358286062507551, -53865503179448478605, -1880864793407486366353

Offset

0,4

Comments

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..124

Formula

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

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

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

Example

A109253(n)/(n!*2^n) ~ (1 - 1/(2*n) - 1/(4*n^2) - 5/(8*n^3) - 35/(16*n^4) - ...
A112225(n)/(n!*2^(n-1)) ~ (1 - 1/(2*n) - 1/(4*n^2) - 5/(8*n^3) - 35/(16*n^4) - ...

Crossrefs

Cf. A109253, A112225.

Sequence in context: A102147 A051577 A124564 * A349515 A362356 A307679

Adjacent sequences: A260949 A260950 A260951 * A260953 A260954 A260955

Keyword

sign

Author

Vaclav Kotesovec, Aug 05 2015

Status

approved