A356960
E.g.f. satisfies: A(x) = 1/(1 - x * A(x)^3)^A(x).
Original entry on oeis.org
1, 1, 10, 207, 6620, 288040, 15891234, 1063219640, 83665143176, 7572321823536, 775010639465040, 88510236140283672, 11158965455394331992, 1539441941412714237912, 230675631266761375815288, 37309025609545822539225240, 6478248637390494598048444224
Offset: 0
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a[n_] := Sum[(3*n + k + 1)^(k - 1)*Abs[StirlingS1[n, k]], {k, 0, n}] (* Sidney Cadot, Jan 05 2023 *)
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a(n) = sum(k=0, n, (3*n+k+1)^(k-1)*abs(stirling(n, k, 1)));
A356972
E.g.f. satisfies log(A(x)) = (exp(x * A(x)^2) - 1) * A(x).
Original entry on oeis.org
1, 1, 8, 128, 3139, 104382, 4393590, 224045271, 13428576766, 925335827928, 72082558060889, 6264277731652096, 600873473776204782, 63059026039778220285, 7187299097301622432156, 884141943373486896560252, 116756337165196381259759707, 16474480747756013055963484442
Offset: 0
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a(n) = sum(k=0, n, (2*n+k+1)^(k-1)*stirling(n, k, 2));
A357011
E.g.f. satisfies A(x) * log(A(x)) = exp(x * A(x)^3) - 1.
Original entry on oeis.org
1, 1, 6, 74, 1407, 36357, 1190476, 47254783, 2205546706, 118378505742, 7184030384361, 486440226752911, 36358328607088010, 2973464028723984551, 264119772408892921774, 25321946948812001539166, 2606224408648404660237647, 286624141573198517220290837
Offset: 0
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a(n) = sum(k=0, n, (3*n-k+1)^(k-1)*stirling(n, k, 2));
Showing 1-3 of 3 results.