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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001
STATUS
approved