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A002510
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Expansion of a modular function for Gamma_0(15).
(Formerly M1825 N0725)
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 6,3
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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).
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FORMULA
| eta(15z)^13/(eta(z)*eta(3z)^5*eta(5z)^7)
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
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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..41); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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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 */
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CROSSREFS
| Sequence in context: A127219 A122208 A106358 * A102943 A062880 A066707
Adjacent sequences: A002507 A002508 A002509 * A002511 A002512 A002513
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jan 14 2001
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