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 A000713 EULER transform of 3, 2, 2, 2, 2, 2, 2, 2, ... (Formerly M2731 N1096) 7
 1, 3, 8, 18, 38, 74, 139, 249, 434, 734, 1215, 1967, 3132, 4902, 7567, 11523, 17345, 25815, 38045, 55535, 80377, 115379, 164389, 232539, 326774, 456286, 633373, 874213, 1200228, 1639418, 2228546, 3015360, 4062065, 5448995, 7280060, 9688718, 12846507, 16972577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals row sums of triangle A146023. - Gary W. Adamson, Oct 26 2008 Partial sums of A000712. - Geoffrey Critzer, Apr 19 2012, corrected by Omar E. Pol, Jun 19 2012 Equals the number of partitions of n with 1's of three kinds and all parts >1 of two kinds. - Gregory L. Simay, Mar 25 2018 REFERENCES H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122. 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). LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 390 N. J. A. Sloane, Transforms FORMULA G.f.: A(x)/(1-x) where A(x) is g.f. for A000712. - Geoffrey Critzer, Apr 19 2012. From Vaclav Kotesovec, Aug 16 2015: (Start) a(n) ~ sqrt(3*n)/Pi * A000712(n). a(n) ~ exp(2*Pi*sqrt(n/3)) / (4*Pi*3^(1/4)*n^(3/4)). (End) G.f.: exp(Sum_{k>=1} (2*sigma_1(k) + 1)*x^k/k). - Ilya Gutkovskiy, Aug 21 2018 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-> `if`(n<2, 3, 2)): seq(a(n), n=0..40); # Alois P. Heinz, Sep 08 2008 MATHEMATICA nn=20; g=Product[1/(1-x^i), {i, 1, nn}]; c=1/(1-x); CoefficientList[Series[g^2/(1-x), {x, 0, nn}], x] (* Geoffrey Critzer, Apr 19 2012 *) PROG (PARI) x='x+O('x^66); Vec(1/((1-x)*eta(x)^2)) \\ Joerg Arndt, May 01 2013 CROSSREFS Cf. A000716. Row sums of triangle A093010. Cf. A146023. - Gary W. Adamson, Oct 26 2008 Sequence in context: A136376 A099845 A036635 * A261325 A261446 A078409 Adjacent sequences:  A000710 A000711 A000712 * A000714 A000715 A000716 KEYWORD nonn AUTHOR EXTENSIONS Extended with formula from Christian G. Bower, Apr 15 1998 Definition changed by N. J. A. Sloane, Aug 15 2006 STATUS approved

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Last modified October 15 15:14 EDT 2019. Contains 328030 sequences. (Running on oeis4.)