A367158
E.g.f. satisfies A(x) = 1 - A(x)^3 * log(1 - x).
Original entry on oeis.org
1, 1, 7, 92, 1824, 48804, 1649724, 67492872, 3243567552, 179139978072, 11181615816216, 778466939121552, 59811143359463952, 5027200928936108064, 458865351655379262432, 45201262487568977507328, 4779609140451030860102400, 539990133396500652971120640
Offset: 0
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Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
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a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*abs(stirling(n, k, 1)));
A367155
E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x).
Original entry on oeis.org
1, 1, 5, 56, 948, 21804, 634284, 22348584, 925322784, 44039346264, 2369167375656, 142173632632272, 9416315321258928, 682290228636729504, 53689645309437175968, 4559660591348115191808, 415683140400707316145920, 40490500091575002629253120
Offset: 0
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Table[Sum[(3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
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a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*stirling(n, k, 1));
A367164
E.g.f. satisfies A(x) = 1 + A(x)^3 * (1 - exp(-x)).
Original entry on oeis.org
1, 1, 5, 55, 929, 21271, 616265, 21624415, 891671009, 42263854471, 2264336600825, 135325966276975, 8926057815521489, 644116254555006871, 50477965058305364585, 4269330999037434100735, 387619447676360230226369, 37602089272441407334114471
Offset: 0
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Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS2[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
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a(n) = sum(k=0, n, (-1)^(n-k)*(3*k)!/(2*k+1)!*stirling(n, k, 2));
A377451
E.g.f. satisfies A(x) = 1/(1 - A(x)^4 * (exp(x) - 1)).
Original entry on oeis.org
1, 1, 11, 241, 8171, 377401, 22118531, 1572752161, 131565858491, 12661132904521, 1378019469008051, 167374385250354481, 22443998566390975211, 3293411316452536046041, 524941525063836265071971, 90316250360918785641307201, 16682672480771981403086626331, 3292860351837963891732540729961
Offset: 0
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a(n) = sum(k=0, n, (5*k)!/(4*k+1)!*stirling(n, k, 2));
A377450
E.g.f. satisfies A(x) = 1/(1 - A(x)^3 * (exp(x) - 1)).
Original entry on oeis.org
1, 1, 9, 157, 4209, 153301, 7075209, 395858317, 26043658209, 1970447255941, 168569253106809, 16090431675455677, 1695423031884496209, 195469637688003331381, 24477403062879209570409, 3308367753565825806208237, 480047805083610542972470209, 74429414765710201956179803621
Offset: 0
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a(n) = sum(k=0, n, (4*k)!/(3*k+1)!*stirling(n, k, 2));
A377452
E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x) - 1))^2.
Original entry on oeis.org
1, 2, 16, 224, 4612, 126392, 4340836, 179534504, 8693925172, 482731239032, 30243460133956, 2110849596096584, 162438922745208532, 13665129603889106072, 1247684652874279407076, 122885960933254703151464, 12987106624622962667192692, 1466014441678589235669027512
Offset: 0
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a(n) = 2*sum(k=0, n, (3*k+1)!/(2*k+2)!*stirling(n, k, 2));
A377717
E.g.f. satisfies A(x) = (1 + (exp(x) - 1) * A(x))^3.
Original entry on oeis.org
1, 3, 27, 405, 8703, 245493, 8608167, 361640205, 17727268383, 993980112453, 62774530115607, 4410751512076605, 341353603094403663, 28856102576884010613, 2645807719152819131847, 261551674681092859354605, 27732033282190658330940543, 3139533157528775981685527973
Offset: 0
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a(n) = 3*sum(k=0, n, (3*k+2)!/(2*k+3)!*stirling(n, k, 2));
Showing 1-7 of 7 results.