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Search: id:A002300
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| A002300 |
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Coefficients in the expansion of B^2*C^3 in Watson's notation of page 118.
(Formerly M0093 N0029)
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+0
3
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| 1, -2, -1, 2, 1, 2, -2, -3, 4, 1, -5, -3, -6, 8, 3, 4, 8, -3, 0, -2, -8, -4, -4, -13, 9, 5, 18, -2, -2, -8, -3, 10, 0, -4, 2, 19, -14, 7, -8, 0, -20, -4, -1, 8, -2, -15, -7, 8, 26, -10, 26, 18, 10, -2, 10, -28, -29, 18, -20, -15, 6, -8, 8, -8, 2, 19, -1, 0, -8, -6, 28, -26, -6, 23, -1, 4, 12, 25, -36, -14, 8, 0, 18, 20, 21, -12, -3, -9, 0, -16, -48
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Although Watson says these are the coefficients theta_n defined on page 128, it appears that this is a mistake, and they are really the coefficients theta'_n. The true theta_n are given in A160528.
Watson's main reason for computing this sequence was to study values of n such that partition(49n+47) == 0 mod 343 (cf. A160553).
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REFERENCES
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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).
Watson, G. N.; Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128. See p. 128.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..199
GDZ, Digitized volumes of Crelle [Added by N. J. A. Sloane, Nov 13, 2009]
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FORMULA
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See Maple code for formula.
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EXAMPLE
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x^23-2*x^47-x^71+2*x^95+x^119+2*x^143-2*x^167-3*x^191+4*x^215+x^239-...
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MAPLE
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M1:=2400:
fm:=mul(1-x^n, n=1..M1):
B:=x*subs(x=x^24, fm):
C:=x^7*subs(x=x^168, fm):
t1:=B^2*C^3;
t2:=series(t1, x, M1);
t3:=subs(x=y^(1/24), t2/x^23);
t4:=series(t3, y, M1/24);
t5:=seriestolist(t4); # A002300
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CROSSREFS
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Cf. A160553.
Sequence in context: A161054 A161258 A161283 this_sequence A049099 A143179 A089610
Adjacent sequences: A002297 A002298 A002299 this_sequence A002301 A002302 A002303
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KEYWORD
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sign,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Nov 14 2009
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