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Expansion of e.g.f. 1 / (1 + log(1 - 4*x))^(1/4).
0

%I #8 Nov 18 2023 08:36:11

%S 1,1,9,137,2929,80689,2722745,108817785,5028704865,263891635425,

%T 15505410046185,1008591244314345,71960155841683665,

%U 5587928499550175505,469183592107676627865,42356983967876631615705,4091474631070907136246465,421070307443746576367920065

%N Expansion of e.g.f. 1 / (1 + log(1 - 4*x))^(1/4).

%F a(n) = Sum_{k=0..n} 4^(n-k) * (Product_{j=0..k-1} (4*j+1)) * |Stirling1(n,k)|.

%F a(0) = 1; a(n) = Sum_{k=1..n} 4^k * (1 - 3/4 * k/n) * (k-1)! * binomial(n,k) * a(n-k).

%o (PARI) a(n) = sum(k=0, n, 4^(n-k)*prod(j=0, k-1, 4*j+1)*abs(stirling(n, k, 1)));

%Y Cf. A352073.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 18 2023