A356402 - OEIS

%I #10 Aug 05 2022 10:48:20

%S 1,1,3,16,86,626,5267,50793,543279,6544805,86503762,1242678141,

%T 19259416827,321457169151,5736414618209,108931865485750,

%U 2191495621647324,46604972526167314,1043844453093239627,24555321244430950299,605239630722584461955,15600222966916650541099

%N Expansion of e.g.f. ( Product_{k>0} (1+x^k)^(1/k!) )^(1/(1-x)).

%F a(0) = 1; a(n) = Sum_{k=1..n} A356401(k) * binomial(n-1,k-1) * a(n-k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^(1/k!))^(1/(1-x))))

%o (PARI) a356401(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!)));

%o a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356401(j)*binomial(i-1, j-1)*v[i-j+1])); v;

%Y Cf. A298906, A356025, A356392, A356401.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 05 2022