This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A000291 M1168 N0447 #69 Jan 01 2024 08:00:55
%S A000291 2,4,9,16,29,47,77,118,181,267,392,560,797,1111,1541,2106,2863,3846,
%T A000291 5142,6808,8973,11733,15275,19753,25443,32582,41569,52770,66757,84078,
%U A000291 105555,131995,164566,204450,253292,312799,385285,473183,579722,708353,863553
%N A000291 Number of bipartite partitions of n white objects and 2 black ones.
%C A000291 Number of ways to factor p^n*q^2 where p and q are distinct primes.
%C A000291 a(n) is the number of multiset partitions of the multiset {r^n, s^2}. - _Joerg Arndt_, Jan 01 2024
%D A000291 M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956, p. 1.
%D A000291 Amarnath Murthy, "Generalization of Smarandache Factor Partition introducing Smarandache Factor Partition". Smarandache Notions Journal, 1-2-3, vol. 11, 2000.
%D A000291 Amarnath Murthy, Program for finding out the number of Smarandache Factor Partitions. Smarandache Notions Journal, Vol. 13, 2002.
%D A000291 Amarnath Murthy, e-book, MS LIT format, "Ideas on Smarandache Notions".
%D A000291 Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; USA 2005. See Section 1.9, 1.14.
%D A000291 D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778. - _N. J. A. Sloane_, Dec 30 2018
%D A000291 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000291 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000291 Alois P. Heinz and Vaclav Kotesovec, <a href="/A000291/b000291.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..5000 from Alois P. Heinz)
%H A000291 F. C. Auluck, <a href="http://dx.doi.org/10.1017/S0305004100028061">On partitions of bipartite numbers</a>, Proc. Cambridge Philos. Soc. 49, (1953). 72-83.
%H A000291 F. C. Auluck, <a href="/A002774/a002774.pdf">On partitions of bipartite numbers, annotated scan of a few pages.</a>
%H A000291 M. S. Cheema and H. Gupta, <a href="/A002755/a002755.pdf">Tables of Partitions of Gaussian Integers</a>, National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956. (Annotated scanned pages from, plus a review)
%F A000291 a(n) = if n <= 2 then A054225(2,n) else A054225(n,2). - _Reinhard Zumkeller_, Nov 30 2011
%F A000291 From _Vaclav Kotesovec_, Feb 01 2016, corrected Nov 05 2016: (Start)
%F A000291 a(n) = A000070(n) + A000097(n).
%F A000291 a(n) ~ sqrt(3) * exp(Pi*sqrt(2*n/3)) / (4*Pi^2) * (1 + 83*Pi/(24*sqrt(6*n))).
%F A000291 (End)
%e A000291 a(2) = 9: let p = 2 and q = 3, p^2*q^2 = 36; there are 9 factorizations: (36), (18*2), (12*3), (9*4), (9*2^2), (6*6), (6*3*2), (4*3^2), (3^2*2^2).
%t A000291 max = 40; col = 2; s1 = Series[Product[1/(1-x^(n-k)*y^k), {n, 1, max+2}, {k, 0, n}], {y, 0, col}] // Normal; s2 = Series[s1, {x, 0, max+1}]; a[n_] := SeriesCoefficient[s2, {x, 0, n}, {y, 0, col}]; Table[ a[n] , {n, 0, max}] (* _Jean-François Alcover_, Mar 13 2014 *)
%t A000291 nmax = 50; CoefficientList[Series[1/(1-x)*(1 + 1/(1-x^2))*Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 01 2016 *)
%Y A000291 Column 2 of A054225.
%Y A000291 Cf. A005380.
%K A000291 nonn
%O A000291 0,1
%A A000291 _N. J. A. Sloane_
%E A000291 Edited by _Christian G. Bower_, Jan 08 2004