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));
A355762
E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^2.
Original entry on oeis.org
1, 1, 8, 125, 2987, 96727, 3963841, 196769897, 11480304448, 770031502467, 58386951857583, 4938864464154469, 461111056016847137, 47101341445053180079, 5225323162578044669492, 625646891309723527419137, 80416734865584980392853799, 11044230667889978466327860347
Offset: 0
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a(n) = sum(k=0, n, (n+2*k+1)^(k-1)*stirling(n, k, 2));
A357350
E.g.f. satisfies A(x) = log(1 + x * exp(A(x))) * exp(2 * A(x)).
Original entry on oeis.org
0, 1, 5, 62, 1210, 32464, 1109988, 46159364, 2261784880, 127625290704, 8150589862080, 581192861530368, 45772039038334464, 3945903751253912928, 369585982325018567808, 37372951572516507717120, 4057994343926975346772992, 470900282395259211311765760
Offset: 0
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a(n) = sum(k=1, n, (n+2*k)^(k-1)*stirling(n, k, 1));
A367199
E.g.f. satisfies A(x) = (1 + x*A(x))^(A(x)^3).
Original entry on oeis.org
1, 1, 8, 141, 3852, 143460, 6780642, 388851960, 26235133992, 2036243259648, 178742696099040, 17509589369568648, 1893647907646728120, 224106838102512869400, 28809018473999642686584, 3997516614926297143604760, 595518793080901690966354368
Offset: 0
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a(n) = sum(k=0, n, (n+3*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.