A335157 Define b(n) by 1/sm(w) = Sum_{n >= 0} b(3*n-1)*w^(3*n-1), where sm(w) is the elliptic function defined in A104133; a(n) = numerator of b(3*n-1).

1, 1, -1, -1, 11, 1, -193, -5, 3851, 449, -16493, -17093, 2776513483, 2766847, -18326878991, -284903947, 313476755027, 15306883537, -5759963886461, -549822999679, 43471527926977757, 649802711643571, -53651420037921807347, -278016083032863199, 164833044827776566977996843

Offset

0,5

Comments

Note that the expansions of 1/sm(w) and cm(w)/sm(w) on page 4 of the Adams reference agree apart from signs.

References

Oscar S. Adams, Elliptic Functions Applied to Conformal World Maps, Special Publication No. 112 of the U.S. Coast and Geodetic Survey, 1925. See pp. 3-4.

Links

Table of n, a(n) for n=0..24.

Example

1/sm(w) = w^(-1) + (1/6)*w^2 - (1/252)*w^5 - (1/4536)*w^8 + (11/2476656)*w^11 + (1/3714984)*w^14 - (193/35574686784)*w^17 - (5/15246294336)*w^20 + (3851/582713369521920)*w^23 + (449/1123804355506560)*w^26 - ...

Prog

(PARI) anum(nn) = my(A = O(x)); for(i=0, nn, A = intformal( (1 - intformal(A^2))^2) ); my(v=Vec(1/A)); apply(x->numerator(x), vector(#v\3, k, v[3*k-2]));

Crossrefs

Cf. A104133 (sm), A104134 (cm), A335158 (denominators).

See also A335180, A335181.

Sequence in context: A038315 A218018 A093158 * A330077 A132098 A223513

Adjacent sequences: A335154 A335155 A335156 * A335158 A335159 A335160

Keyword

sign,frac

Author

Michel Marcus and N. J. A. Sloane, Jun 08 2020.

Status

approved