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A349556
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E.g.f. satisfies: A(x) = 1/(1 - x*A(x))^A(x).
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11
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1, 1, 6, 69, 1196, 27900, 820554, 29168048, 1216826120, 58301363808, 3155539049040, 190434409300872, 12679792851087768, 923409652630222680, 73016802381788896344, 6230201355664856039640, 570574779781503603910464, 55826084651771645745562368
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..17.
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FORMULA
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a(n) = Sum_{k=0..n} (n+k+1)^(k-1) * |Stirling1(n,k)|.
a(n) ~ s^2 * sqrt((1 - r*s) / (1 + r*s*(s-1) * (2 - r*s))) * n^(n-1) / (exp(n) * r^(n - 1/2)), where r = 0.1591040778917510493879632960549533860431737829556... and s = 1.588466710327904339474066925768589168215650366378... are real roots of the system of equations 1/s = (1 - r*s)^s, r*s/(1 - r*s) - log(1 - r*s) = 1/s. - Vaclav Kotesovec, Nov 22 2021
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MATHEMATICA
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a[n_] := Sum[(n + k + 1)^(k - 1) * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Nov 22 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (n+k+1)^(k-1)*abs(stirling(n, k, 1)));
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CROSSREFS
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Cf. A052813, A162655, A349559.
Sequence in context: A177751 A338176 A235327 * A098639 A305110 A235328
Adjacent sequences: A349553 A349554 A349555 * A349557 A349558 A349559
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Nov 21 2021
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STATUS
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approved
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