A099059 The odd bisection of A000594.

1, 252, 4830, -16744, -113643, 534612, -577738, 1217160, -6905934, 10661420, -4219488, 18643272, -25499225, -73279080, 128406630, -52843168, 134722224, -80873520, -182213314, -145589976, 308120442, -17125708, -548895690, 2687348496, -1696965207, -1740295368, -1596055698

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Mathew Rogers, Identities for the Ramanujan zeta function, arXiv:1210.1942 [math.NT], 2012-2013. See page 3 Lemma 1.

Formula

Expansion of (F(q) - F(-q)) / 2 = F(q) + 24*F(q^2) + 2048*F(q^4) in powers of q^2 where F() is the g.f. of A000594. - Michael Somos, Apr 17 2015

a(n) = A000594(2*n + 1). - Michael Somos, Apr 17 2015

Example

G.f. = 1 + 252*x + 4830*x^2 - 16744*x^3 - 113643*x^4 + 534612*x^5 + ...
G.f. = q + 252*q^3 + 4830*q^5 - 16744*q^7 - 113643*q^9 + 534612*q^11 + ...

Mathematica

a[ n_] := SeriesCoefficient[ q QPochhammer[q]^24, {q, 0, 2 n + 1}]; (* Michael Somos, Apr 17 2015 *)
a[n_] := RamanujanTau[2*n+1]; Array[a, 30, 0] (* Amiram Eldar, Jan 10 2025 *)

Prog

(PARI) {a(n) = if( n<0, 0, n = 2*n+1; polcoeff( x * eta(x + x * O(x^n))^24, n))}; /* Michael Somos, Apr 17 2015 */

Crossrefs

Cf. A000594, A099060.

Sequence in context: A218418 A184498 A169713 * A151610 A250085 A024018

Adjacent sequences: A099056 A099057 A099058 * A099060 A099061 A099062

Keyword

sign

Author

N. J. A. Sloane, Nov 15 2004

Extensions

More terms from Joshua Zucker, May 15 2006

Status

approved