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));
A349589
E.g.f. satisfies: A(x) * log(A(x)) = 1 - exp(-x*A(x)).
Original entry on oeis.org
1, 1, 0, -4, -3, 87, 230, -4583, -27216, 434928, 4871719, -62913079, -1240374960, 12230778601, 426135019232, -2759957884648, -189393687667107, 479371576805751, 105233549909615798, 233116575802412969, -71022416772836562008, -574100485456271792020
Offset: 0
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a[n_] := Sum[(-1)^(n - k)*(n - k + 1)^(k - 1)*StirlingS2[n, k], {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, Nov 23 2021 *)
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a(n) = sum(k=0, n, (-1)^(n-k)*(n-k+1)^(k-1)*stirling(n, k, 2));
A357423
E.g.f. satisfies A(x) * exp(A(x)) = log(1 + x * exp(A(x))).
Original entry on oeis.org
0, 1, -1, -1, 10, 4, -384, 818, 29800, -205200, -3612000, 56042832, 556589232, -19091774352, -70128589608, 8044430218680, -25379500932864, -4055729067351552, 48310659088501248, 2334746679051721536, -58078273556262804480, -1420062892415588203776
Offset: 0
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a(n) = sum(k=1, n, (n-k)^(k-1)*stirling(n, k, 1));
A349600
E.g.f. satisfies: A(x)^A(x) = 1 + x*A(x)^2.
Original entry on oeis.org
1, 1, 2, 3, -20, -320, -2274, 5474, 487432, 8358480, 37944240, -2286868848, -81319780200, -1139790073968, 18382692073032, 1570867988794680, 42704382709868736, 55662087673489920, -49662902468183117760, -2360239974764654675904, -38098700311039336972800
Offset: 0
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a(n) = sum(k=0, n, (2*n-k+1)^(k-1)*stirling(n, k, 1));
A355768
E.g.f. satisfies A(x)^(A(x)^2) = 1 + x*A(x).
Original entry on oeis.org
1, 1, -2, 6, -28, 260, -3948, 71120, -1392368, 29971008, -724981920, 19800726528, -603571233120, 20210951379840, -734663902256256, 28785160833254400, -1210241780559067392, 54390280325210271744, -2602745536670709682176, 132118736078618372579328
Offset: 0
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a(n) = sum(k=0, n, (n-2*k+1)^(k-1)*stirling(n, k, 1));
Showing 1-5 of 5 results.