cp's OEIS Frontend

A003292 Number of 4-line partitions of n decreasing across rows.

%I A003292 M1050 #36 Oct 13 2017 12:18:00
%S A003292 1,2,4,7,11,19,29,46,70,106,156,232,334,482,686,971,1357,1894,2612,
%T A003292 3592,4900,6656,8980,12077,16137,21490,28476,37600,49422,64763,84511,
%U A003292 109953,142539,184244,237368,304996,390688,499189,636059,808489,1025017,1296595,1636173,2060246,2588440,3245381,4060519,5070574
%N A003292 Number of 4-line partitions of n decreasing across rows.
%C A003292 a(n) is the number of unlabeled graphs on n nodes whose connected components are a path or a cycle. - _Geoffrey Critzer_, Nov 28 2011
%D A003292 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A003292 Herbert S. Wilf, Generatingfunctiontology, Academic Press, 1994, page 106.
%H A003292 Vincenzo Librandi, <a href="/A003292/b003292.txt">Table of n, a(n) for n = 1..1000</a>
%H A003292 M. S. Cheema and W. E. Conway, <a href="http://dx.doi.org/10.1090/S0025-5718-1972-0314756-0">Numerical investigation of certain asymptotic results in the theory of partitions</a>, Math. Comp., 26 (1972), 999-1005.
%F A003292 G.f.: Product (1 - x^k)^-{c(k)}; c(k) = 1, 1, 2, 2, 2, 2, ....
%t A003292 Rest[p=Product[1/(1 - x^i), {i, 1, 20}]; CoefficientList[Series[p^2 (1 - x) (1 - x^2), {x, 0, 20}], x]] (* _Geoffrey Critzer_, Nov 28 2011 *) (* adapted by _Vincenzo Librandi_, Oct 12 2017 *)
%o A003292 (PARI)  \\ program includes a(0) = 1:
%o A003292 c(n) = 1 + (n>=3);
%o A003292 N = 66;  x = 'x + O('x^N);
%o A003292 Vec( 1 / prod(n=1, N, (1 - x^k)^c(n)) )  \\ _Joerg Arndt_, Oct 12 2017
%K A003292 nonn,easy
%O A003292 1,2
%A A003292 _N. J. A. Sloane_
%E A003292 More terms from _Joerg Arndt_, Oct 12 2017