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 A378424 #27 Dec 06 2024 11:16:31
%S A378424 1,2,3,10,25,78,245,810,2700,9250,32065,112710,400023,1432858,5170575,
%T A378424 18784170,68635477,252088416,930138521,3446167850,12815663595,
%U A378424 47820447026,178987624513,671825132838,2528212128750,9536895064398,36054433807398,136583761444354,518401146543811,1971076361996550,7506908923471953,28634752211620266
%N A378424 Product_{n>=1} (1+x^n)^a(n) = Sum_{k>=0} C(k)*x^k, where C(k) = A000108(k).
%C A378424 Conjecture: A327937(n) divides a(n).
%F A378424 Inverse Euler transform of A179277.
%o A378424 (PARI)
%o A378424 A179277(n) = if(n<=1, 1, sum(k=0,floor(n/2),A179277(k)*binomial(2*n-4*k, n-2*k)/(n-2*k+1)))
%o A378424 a(max_n) = {my(va,vb,vc); vc=va=vector(max_n);vb = vector(max_n,k,A179277(k)); for(k=1,max_n,vc[k]=k*vb[k]-sum(m=1,k-1,vc[m]*vb[k-m])); for(k=1,max_n,va[k]=1/k*sumdiv(k,m,moebius(k/m)*vc[m])); va;}
%Y A378424 Cf. A000108, A157161, A179277, A327937.
%K A378424 nonn
%O A378424 1,2
%A A378424 _Thomas Scheuerle_, Nov 26 2024