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A002510 Expansion of a modular function for Gamma_0(15).
(Formerly M1825 N0725)
1
1, 1, 2, 8, 10, 24, 53, 74, 153, 280, 436, 793, 1322, 2085, 3510, 5648, 8796, 14042, 21921, 33490, 51796, 78843, 118108, 178029, 265225, 390852, 576946, 843694, 1224329, 1775450, 2556360, 3658111, 5224159, 7418887, 10481780, 14773012, 20723154, 28941023 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,3

REFERENCES

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

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. [Annotated scanned copy, barely legible]

FORMULA

Expansion of eta(q^15)^13 / (eta(q) * eta(q^3)^5 * eta(q^5)^7) in powers of q.

Expansion of (c(q^5)^2 / (3 * c(q)))^2 / (b(q) * b(q^5)) in powers of q where b(), c() are cubic AGM theta functions. - Michael Somos, Jun 10 2012

Euler transform of period 15 sequence [1, 1, 6, 1, 8, 6, 1, 1, 6, 8, 1, 6, 1, 1, 0, ...]. - Michael Somos, Nov 10 2005

a(n) ~ exp(4*Pi*sqrt(2*n/15)) / (2^(1/4) * 3^(17/4) * 5^(13/4) * n^(3/4)). - Vaclav Kotesovec, Apr 09 2018

EXAMPLE

q^6 + q^7 + 2*q^8 + 8*q^9 + 10*q^10 + 24*q^11 + 53*q^12 + 74*q^13 + 153*q^14 + ...

MAPLE

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: aa:=etr(n-> [1, 1, 6, 1, 8, 6, 1, 1, 6, 8, 1, 6, 1, 1, 0] [modp(n-1, 15)+1]): a:=n-> aa(n-6): seq(a(n), n=6..42); # Alois P. Heinz, Sep 08 2008

MATHEMATICA

etr[p_] := Module[{b}, b[n_] := b[n] = Module[{d, j}, If[n == 0, 1, Sum [Sum [d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]]; b]; aa = etr[ Function[n, {1, 1, 6, 1, 8, 6, 1, 1, 6, 8, 1, 6, 1, 1, 0}[[Mod[n-1, 15] + 1]]]]; a[n_] := aa[n-6]; Table[a[n], {n, 6, 41}] (* Jean-Fran├žois Alcover, Mar 03 2014, after Alois P. Heinz *)

PROG

(PARI) {a(n) = local(A); if( n<6, 0, n -= 6; A = x * O(x^n); polcoeff( eta(x^15 + A)^13 / (eta(x + A) * eta(x^3 + A)^5 * eta(x^5 + A)^7), n))} /* Michael Somos, Nov 10 2005 */

CROSSREFS

Sequence in context: A297475 A106358 A209449 * A247592 A102943 A062880

Adjacent sequences:  A002507 A002508 A002509 * A002511 A002512 A002513

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

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Last modified August 19 15:50 EDT 2018. Contains 313878 sequences. (Running on oeis4.)