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)));
A367161
E.g.f. satisfies A(x) = 1 + A(x)^3 * (exp(x) - 1).
Original entry on oeis.org
1, 1, 7, 91, 1795, 47851, 1612027, 65731891, 3148530595, 173319612571, 10782796483147, 748237171338691, 57299882326956595, 4800323120225595691, 436719009263680421467, 42878536726317406241491, 4519124182661042439577795, 508885588456024192452993211
Offset: 0
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Table[Sum[(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, (3*k)!/(2*k+1)!*stirling(n, k, 2));
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));
A367156
E.g.f. satisfies A(x) = 1 + A(x)^2 * log(1 + x*A(x)).
Original entry on oeis.org
1, 1, 5, 53, 862, 19024, 531520, 17991630, 715803832, 32740331784, 1692869465304, 97648275936672, 6216826224534624, 433030023365176704, 32757854472395131776, 2674517780432621462640, 234408432378333868580736, 21951787708820941049727360
Offset: 0
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Table[Sum[(n + 2*k)!/(n + k + 1)!*StirlingS1[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 07 2023 *)
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a(n) = sum(k=0, n, (n+2*k)!/(n+k+1)!*stirling(n, k, 1));
Showing 1-4 of 4 results.