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A367426
Expansion of e.g.f. 1 / (1 + log(1 - 4*x))^(1/4).
0
1, 1, 9, 137, 2929, 80689, 2722745, 108817785, 5028704865, 263891635425, 15505410046185, 1008591244314345, 71960155841683665, 5587928499550175505, 469183592107676627865, 42356983967876631615705, 4091474631070907136246465, 421070307443746576367920065
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} 4^(n-k) * (Product_{j=0..k-1} (4*j+1)) * |Stirling1(n,k)|.
a(0) = 1; a(n) = Sum_{k=1..n} 4^k * (1 - 3/4 * k/n) * (k-1)! * binomial(n,k) * a(n-k).
PROG
(PARI) a(n) = sum(k=0, n, 4^(n-k)*prod(j=0, k-1, 4*j+1)*abs(stirling(n, k, 1)));
CROSSREFS
Cf. A352073.
Sequence in context: A081876 A139760 A112702 * A296394 A367246 A322576
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 18 2023
STATUS
approved