A349588
E.g.f. satisfies: A(x) * log(A(x)) = exp(x*A(x)) - 1.
Original entry on oeis.org
1, 1, 2, 8, 47, 367, 3592, 42317, 583522, 9223872, 164482761, 3267077365, 71540314562, 1712334954865, 44479256704898, 1246241906483516, 37465750470667023, 1202986323660907447, 41089436549405467096, 1487622596267089224901, 56907111260864275384346
Offset: 0
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a[n_] := Sum[(n - k + 1)^(k - 1)*StirlingS2[n, k], {k, 0, n}]; Array[a, 21, 0] (* Amiram Eldar, Nov 23 2021 *)
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a(n) = sum(k=0, n, (n-k+1)^(k-1)*stirling(n, k, 2));
A349587
E.g.f. satisfies: A(x)^A(x) = 1 + x*A(x).
Original entry on oeis.org
1, 1, 0, -3, 4, 60, -294, -2800, 34504, 197568, -6087360, -9146808, 1488986808, -5886157992, -469973309064, 5492298353880, 177826238321856, -4277426240130048, -72353540601814464, 3537861051231290880, 22847222673714931200, -3226666120379253611136
Offset: 0
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a[n_] := Sum[(n - k + 1)^(k - 1)*StirlingS1[n, k], {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, Nov 23 2021 *)
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a(n) = sum(k=0, n, (n-k+1)^(k-1)*stirling(n, k, 1));
A349602
E.g.f. satisfies: A(x) * log(A(x)) = 1 - exp(-x*A(x)^2).
Original entry on oeis.org
1, 1, 2, 2, -43, -668, -5908, -1209, 1399400, 37121106, 508366819, -3012861630, -444910083132, -15407930598279, -249403814792546, 5359691081465462, 589889204153846141, 23861630070579997032, 379819221897309026072, -21971010821241361939769
Offset: 0
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a[n_] := Sum[(-1)^(n - k)*(2*n - k + 1)^(k - 1)*StirlingS2[n, k], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Nov 23 2021 *)
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a(n) = sum(k=0, n, (-1)^(n-k)*(2*n-k+1)^(k-1)*stirling(n, k, 2));
A355765
E.g.f. satisfies A(x)^2 * log(A(x)) = 1 - exp(-x*A(x)).
Original entry on oeis.org
1, 1, -2, 5, -27, 307, -4403, 71353, -1333090, 28816647, -709090995, 19516306141, -593330123807, 19747569261851, -714304238263502, 27903505800651169, -1170716239531658759, 52503701213718494671, -2506483879112555156467, 126905975195788734150405
Offset: 0
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a(n) = sum(k=0, n, (-1)^(n-k)*(n-2*k+1)^(k-1)*stirling(n, k, 2));
Showing 1-4 of 4 results.