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A002039
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Convolution inverse of A143348.
(Formerly M2465 N0979)
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1
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1, 3, 5, 10, 25, 64, 160, 390, 940, 2270, 5515, 13440, 32735, 79610, 193480, 470306, 1143585, 2781070, 6762990, 16445100, 39987325, 97232450, 236432060, 574915770, 1397981470, 3399360474, 8265943685, 20099618590, 48874630750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Gandhi denotes f(-x) by Phi(x) and a(n) by G(n).
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REFERENCES
| J. M. Gandhi, On numbers related to partitions of a number, Amer. Math. Monthly, 76 (1969), 1033-1036.
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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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| G.f.: -x / (Sum_{k>0} k * (-x)^k / (1 - (-x)^k)) = 1 / (log( f(x) )') where f(-x) = Product_{k>0} (1 - x^k) is one of Ramanujan's theta functions. - Michael Somos, Apr 08 2003
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EXAMPLE
| 1 + 3*x + 5*x^2 + 10*x^3 + 25*x^4 + 64*x^5 + 160*x^6 + 390*x^7 + 940*x^8 + ...
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MATHEMATICA
| max = 28; f[x_] := -x / Sum[ k*(-x)^k/(1-(-x)^k), {k, 1, max+1}]; CoefficientList[ Series[ f[x], {x, 0, max}], x] (* From Jean-François Alcover, Nov 07 2011, after Michael Somos *)
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( 1 / log( eta( -x + x^2 * O(x^n)))', n))} /* Michael Somos Apr 05 2003 */
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CROSSREFS
| Cf. A002040, A143348.
Sequence in context: A173232 A132332 A171867 * A011969 A003187 A003186
Adjacent sequences: A002036 A002037 A002038 * A002040 A002041 A002042
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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