A349556
E.g.f. satisfies: A(x) = 1/(1 - x*A(x))^A(x).
Original entry on oeis.org
1, 1, 6, 69, 1196, 27900, 820554, 29168048, 1216826120, 58301363808, 3155539049040, 190434409300872, 12679792851087768, 923409652630222680, 73016802381788896344, 6230201355664856039640, 570574779781503603910464, 55826084651771645745562368
Offset: 0
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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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a(n) = sum(k=0, n, (n+k+1)^(k-1)*abs(stirling(n, k, 1)));
A356786
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x * A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 92, 510, 15114, 174300, 5558944, 103712616, 3672530280, 96397602840, 3830335035240, 129817630491120, 5796134828193696, 239906921239210680, 11996259216566469120, 584024600798956215360, 32523678395272329425856
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n+k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A356787
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x * A(x)^3).
Original entry on oeis.org
1, 0, 2, 3, 116, 630, 24054, 273000, 11105072, 207213552, 9175467960, 245785969440, 11954556125544, 421832039016960, 22609694372667024, 991695134898861120, 58565049582761702400, 3065736317041568378880, 199024242549235933723200
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n+2*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A356884
E.g.f. satisfies A(x)^A(x) = 1/(1 - x*A(x))^x.
Original entry on oeis.org
1, 0, 2, 3, 20, 150, 1254, 14280, 190000, 2863728, 49465080, 954312480, 20303200488, 473604468480, 12007399511184, 328671680500800, 9663415159357440, 303695188102656000, 10159173955921651776, 360424299614544829440, 13517056067747847719040
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A356885
E.g.f. satisfies A(x)^(A(x)^2) = 1/(1 - x*A(x))^x.
Original entry on oeis.org
1, 0, 2, 3, -4, 30, 954, 6300, 6432, 424872, 18273960, 260682840, 1754408424, 47063118960, 2314149100704, 54798086299320, 773632032345600, 20746972036284480, 1072205580591921600, 36098491880448944640, 816375193722964932480, 25160238159364392336000
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n-3*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A375826
E.g.f. satisfies A(x) = 1/(1 - x*A(x))^(x^2).
Original entry on oeis.org
1, 0, 0, 6, 12, 40, 1260, 11088, 99120, 1926720, 32800320, 535328640, 11274642720, 259872088320, 6108539621184, 158608655251200, 4495317057504000, 134114095312404480, 4253953999500357120, 143971794376985272320, 5141239842495675340800
Offset: 0
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a(n) = n!*sum(k=0, n\3, (n-2*k+1)^(k-1)*abs(stirling(n-2*k, k, 1))/(n-2*k)!);
Showing 1-6 of 6 results.