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 A322211 #31 Apr 10 2025 07:30:15
%S A322211 1,2,10,38,158,602,2382,9142,35492,136936,530404,2053848,7972272,
%T A322211 30977742,120576112,469915012,1833813534,7164469910,28021000340,
%U A322211 109699469798,429850240742,1685728936622,6615913739206,25983523253950,102115250446680,401557335718522,1579978592844064,6219928993470190,24498287876663618,96535916978924934,380568644820360668
%N A322211 a(n) = coefficient of x^n*y^n in Product_{n>=1} 1/(1 - (x^n + y^n)).
%C A322211 Number of subsets of partitions of 2n that have sum n. _Olivier Gérard_, May 07 2020
%H A322211 Paul D. Hanna, <a href="/A322211/b322211.txt">Table of n, a(n) for n = 0..500</a> (previous b-file of terms 0..50 supplied by Vaclav Kotesovec).
%F A322211 Main diagonal of square table A322210.
%F A322211 a(n) ~ c * 4^n / sqrt(Pi*n), where c = 1 / A048651 = 1 / Product_{k>=1} (1 - 1/2^k) = 3.46274661945506361153795734292443116454075790290443839... - _Vaclav Kotesovec_, Dec 23 2018
%e A322211 G.f.: A(x) = 1 + 2*x + 10*x^2 + 38*x^3 + 158*x^4 + 602*x^5 + 2382*x^6 + 9142*x^7 + 35492*x^8 + 136936*x^9 + 530404*x^10 + 2053848*x^11 + 7972272*x^12 + ...
%e A322211 RELATED SERIES.
%e A322211 The product P(x,y) = Product_{n>=1} 1/(1 - (x^n + y^n)) begins
%e A322211 P(x,y) = 1 + (x + y) + (2*x^2 + 2*x*y + 2*y^2) + (3*x^3 + 4*x^2*y + 4*x*y^2 + 3*y^3) + (5*x^4 + 7*x^3*y + 10*x^2*y^2 + 7*x*y^3 + 5*y^4) + (7*x^5 + 12*x^4*y + 18*x^3*y^2 + 18*x^2*y^3 + 12*x*y^4 + 7*y^5) + (11*x^6 + 19*x^5*y + 34*x^4*y^2 + 38*x^3*y^3 + 34*x^2*y^4 + 19*x*y^5 + 11*y^6) + (15*x^7 + 30*x^6*y + 56*x^5*y^2 + 74*x^4*y^3 + 74*x^3*y^4 + 56*x^2*y^5 + 30*x*y^6 + 15*y^7) + (22*x^8 + 45*x^7*y + 94*x^6*y^2 + 133*x^5*y^3 + 158*x^4*y^4 + 133*x^3*y^5 + 94*x^2*y^6 + 45*x*y^7 + 22*y^8) + ...
%e A322211 in which this sequence equals the coefficients of x^n*y^n for n >= 0.
%e A322211 The logarithm of the g.f. begins
%e A322211 log( A(x) ) = 2*x + 16*x^2/2 + 62*x^3/3 + 272*x^4/4 + 922*x^5/5 + 3640*x^6/6 + 12966*x^7/7 + 49872*x^8/8 + 190340*x^9/9 + 745316*x^10/10 + 2928136*x^11/11 + 11602184*x^12/12 + ...
%t A322211 nmax = 20; s = Series[Product[1/(1 - (x^k + y^k)), {k, 1, nmax}], {x, 0, nmax}, {y, 0, nmax}]; Flatten[{1, Table[Coefficient[s, x^n*y^n], {n, 1, nmax}]}] (* _Vaclav Kotesovec_, Dec 04 2018 *)
%o A322211 (PARI)
%o A322211 {P = 1/prod(n=1,61, (1 - (x^n + y^n) +O(x^61) +O(y^61)) );}
%o A322211 {a(n) = polcoeff( polcoeff( P,n,x),n,y)}
%o A322211 for(n=0,35, print1( a(n),", ") )
%Y A322211 Cf. A108796, A258471, A322210, A322213, A322198.
%K A322211 nonn
%O A322211 0,2
%A A322211 _Paul D. Hanna_, Nov 30 2018