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A211971 Column 0 of square array A211970 (in which column 1 is A000041).

%I A211971 #47 May 17 2024 15:25:07
%S A211971 1,1,2,4,6,10,16,24,36,54,78,112,160,224,312,432,590,802,1084,1452,
%T A211971 1936,2568,3384,4440,5800,7538,9758,12584,16160,20680,26376,33520,
%U A211971 42468,53644,67552,84832,106246,132706,165344,205512,254824,315256,389168,479368
%N A211971 Column 0 of square array A211970 (in which column 1 is A000041).
%C A211971 Partial sums give A015128. - _Omar E. Pol_, Jan 09 2014
%H A211971 Vaclav Kotesovec, <a href="/A211971/b211971.txt">Table of n, a(n) for n = 0..10000</a>
%F A211971 a(n) ~ exp(Pi*sqrt(n))*Pi / (16*n^(3/2)) * (1 - (3/Pi + Pi/4)/sqrt(n) + (3/2 + 3/Pi^2+ Pi^2/24)/n). - _Vaclav Kotesovec_, Oct 25 2016, extended Nov 04 2016
%F A211971 G.f.: (1 - x)/theta_4(x), where theta_4() is the Jacobi theta function. - _Ilya Gutkovskiy_, Mar 05 2018
%t A211971 Flatten[{1, Differences[Table[Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}], {n, 0, 60}]]}] (* _Vaclav Kotesovec_, Oct 25 2016 *)
%t A211971 CoefficientList[Series[(1 - x)/EllipticTheta[4, 0, x], {x, 0, 43}], x] (* _Robert G. Wilson v_, Mar 06 2018 *)
%o A211971 (GW-BASIC)' A program with two A-numbers:
%o A211971 10 Dim A008794(100), A057077(100), a(100): a(0)=1
%o A211971 20 For n = 1 to 43: For j = 1 to n
%o A211971 30 If A008794(j+1) <= n then a(n) = a(n) + A057077(j-1)*a(n - A008794(j+1))
%o A211971 40 Next j: Print a(n-1); : Next n
%Y A211971 Cf. A000041, A006950, A008794, A036820, A057077, A195152, A195848, A195849, A195850, A195851, A195852, A196933, A195825, A210964, A277643.
%K A211971 nonn
%O A211971 0,3
%A A211971 _Omar E. Pol_, Jun 10 2012