A363337 - OEIS

%I #16 May 31 2023 10:48:48

%S 1,1,1,1,1,2,2,2,2,3,4,4,4,5,6,7,7,8,10,11,12,14,16,18,19,22,26,29,31,

%T 34,40,45,48,52,60,68,74,80,90,102,111,121,136,152,166,180,201,225,

%U 245,264,294,329,360,387,426,476,521,562,615,683,750,809,883,978,1071,1156,1259,1389,1523

%N G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^(4*k)) * x^k/k ).

%H Seiichi Manyama, <a href="/A363337/b363337.txt">Table of n, a(n) for n = 0..1000</a>

%F A(x) = Sum_{k>=0} a(k) * x^k = 1/Product_{k>=0} (1-x^(4*k+1))^a(k).

%F A(x) * A(i*x) * A(-x) * A(i^3*x) = A(x^4), where i=sqrt(-1).

%F a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( Sum_{d|k and d==1 mod 4} d * a(floor(d/4)) ) * a(n-k).

%o (PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^(4*k))*x^k/k)+x*O(x^n))); Vec(A);

%Y Cf. A000081, A115593, A363336.

%K nonn

%O 0,6

%A _Seiichi Manyama_, May 28 2023