A002511 Expansion of a modular function for Gamma_0(21). (Formerly M1566 N0610)

1, 1, 2, 6, 8, 13, 29, 44, 66, 122, 184, 269, 448, 668, 972, 1505, 2205, 3153, 4677, 6717, 9480, 13656, 19245, 26793, 37714, 52301, 71894, 99392, 135969, 184637, 251492, 339793, 456432, 613837, 820388, 1091154, 1451243, 1920637, 2531468

Offset

6,3

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Morris Newman, Construction and application of a class of modular functions (II). Proc. London Math. Soc. (3) 9 1959 373-387.

Morris Newman, Construction and application of a class of modular functions, II, Proc. London Math. Soc. (3) 9 1959 373-387. [Annotated scanned copy, barely legible]

Formula

Expansion of eta(q^21)^9 / (eta(q) * eta(q^3)^3 * eta(q^7)^5) in powers of q.

Euler transform of period 21 sequence [1, 1, 4, 1, 1, 4, 6, 1, 4, 1, 1, 4, 1, 6, 4, 1, 1, 4, 1, 1, 0, ...]. - Michael Somos, Nov 10 2005

G.f.: x^6 * Product_{k>0} (1 - x^(21*k))^9 / ((1 - x^k) * (1 - x^(3*k))^3 * (1 - x^(7*k))^5). - Michael Somos, Jan 02 2015, corrected by Vaclav Kotesovec, Apr 09 2018

a(n) ~ exp(4*Pi*sqrt(2*n/21)) / (2^(1/4) * 3^(13/4) * 7^(9/4) * n^(3/4)). - Vaclav Kotesovec, Apr 09 2018

Example

G.f. = x^6 + x^7 + 2*x^8 + 6*x^9 + 8*x^10 + 13*x^11 + 29*x^12 + 44*x^13 + ...

Mathematica

QP = QPochhammer; A = x*O[x]^40; s = QP[x^21+A]^9/(QP[x+A]*QP[x^3+A]^3* QP[x^7+A]^5); CoefficientList[s, x] (* Jean-François Alcover, Nov 30 2015, adapted from PARI *)

Prog

(PARI) {a(n) = local(A); if( n<6, 0, n-=6; A = x * O(x^n); polcoeff( eta (x^21 + A)^9 / (eta(x + A) * eta (x^3 + A)^3 * eta (x^7 + A)^5), n))}; /* Michael Somos, Nov 10 2005 */

Crossrefs

Sequence in context: A087327 A266627 A289753 * A074383 A107505 A074400

Adjacent sequences: A002508 A002509 A002510 * A002512 A002513 A002514

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001

Status

approved