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A000706
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Expansion of modular function 1/E_3 (cf. A013973).
(Formerly M5458 N2367)
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0
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1, 504, 270648, 144912096, 77599626552, 41553943041744, 22251789971649504, 11915647845248387520, 6380729991419236488504, 3416827666558895485479576, 1829682703808504464920468048, 979779820147442370107345764512
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| G. H. Hardy and S. Ramanujan, On the coefficients in the expansion of certain modular functions, Proc. Royal Soc., A95 (1918), 144-155 [G. H. Hardy, Coll. Papers, Vol. 1, 294-305.] - Added by N. J. A. Sloane, Feb 21 2010.
S. Ramanujan, Collected Papers of Srinivasa Ramanujan, pp. 115-7, Ed. G. H. Hardy et al., AMS Chelsea 2000, p. 317.
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
| Expansion of Ramanujan's function 1/R(q) in powers of q.
G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= v^2*w^2 +121*u^2*w^2 +4096*u^2*v^2 -8*v^3*w -512*u*v^3 -66*u*v*w^2 +592*u*v^2*w -4224*u^2*v*w. - Michael Somos Aug 09 2007
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PROG
| (PARI) {a(n)= if(n<0, 0, polcoeff( 1/sum(k=1, n, -504*sigma(k, 5)*x^k, 1+x*O(x^n)), n))} /* Michael Somos Aug 09 2007 */
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CROSSREFS
| Convolution inverse of A013973.
Sequence in context: A145095 A035293 A105097 * A068299 A003798 A003791
Adjacent sequences: A000703 A000704 A000705 * A000707 A000708 A000709
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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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