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A000335
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Euler transform of A000292.
(Formerly M3859 N1581)
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3
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1, 5, 15, 45, 120, 331, 855, 2214, 5545, 13741, 33362, 80091, 189339, 442799, 1023192, 2340904, 5302061, 11902618, 26488454, 58479965, 128120214, 278680698, 602009786, 1292027222, 2755684669, 5842618668, 12317175320, 25825429276, 53865355154, 111786084504, 230867856903, 474585792077, 971209629993
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100.
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
| T. D. Noe, Table of n, a(n) for n=1..500
N. J. A. Sloane, Transforms
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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: a:= etr (n-> binomial(n+2, 3)): seq (a(n), n=1..26); [From Alois P. Heinz, Sep 08 2008]
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MATHEMATICA
| max = 33; f[x_] := Exp[ Sum[ x^k/(1-x^k)^4/k, {k, 1, max}]]; Drop[ CoefficientList[ Series[ f[x], {x, 0, max}], x], 1](* From Jean-François Alcover, Nov 21 2011, after Joerg Arndt *)
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PROG
| (PARI) a(n)=if(n<1, 0, polcoeff(exp(sum(k=1, n, x^k/(1-x^k)^4/k, x*O(x^n))), n)) [From Joerg Arndt, Apr 16 2010]
(PARI) /* compute all terms up to N: */
N=66; x='x+O('x^66); /* that many terms */
gf=-1 + exp(sum(k=1, N, x^k/(1-x^k)^4/k));
Vec(gf) /* show terms */ /* Joerg Arndt, Jul 06 2011 */
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CROSSREFS
| Sequence in context: A158875 A022813 A000334 * A200465 A084244 A005030
Adjacent sequences: A000332 A000333 A000334 * A000336 A000337 A000338
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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