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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-François 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 A327988 Adjacent sequences:  A002507 A002508 A002509 * A002511 A002512 A002513 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001 STATUS approved

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Last modified July 27 18:27 EDT 2021. Contains 346308 sequences. (Running on oeis4.)