A357029
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2).
Original entry on oeis.org
1, 0, 0, 6, 36, 210, 3870, 70224, 1122072, 23086344, 586910880, 15469437456, 441107126856, 14206113541152, 496333927370736, 18463733657766144, 739328759822848320, 31759148433997889280, 1447876893211813379520, 69881726567495477445120
Offset: 0
-
m = 20; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x])^(Log[1 - x*A[x]]^2) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
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a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/k!);
A357036
E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) / 2).
Original entry on oeis.org
1, 0, 1, 3, 26, 230, 2794, 39564, 663606, 12712104, 275171106, 6632699040, 176309074644, 5123121177096, 161577261004860, 5497133655605760, 200683752698028924, 7825434930630743616, 324616635150708044796, 14273994548639305751040, 663205761925601097418488
Offset: 0
-
m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = (1 - x*A[x])^(Log[1 - x*A[x]]/2) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
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a(n) = sum(k=0, n\2, (2*k)!*(n+1)^(k-1)*abs(stirling(n, 2*k, 1))/(2^k*k!));
A357090
E.g.f. satisfies A(x) = (1 - x * A(x))^(log(1 - x * A(x)) * A(x)).
Original entry on oeis.org
1, 0, 2, 6, 106, 1060, 21728, 396648, 10174764, 267855264, 8517836832, 289596897480, 11137252365600, 461124747706896, 20922578332613904, 1018268757357253920, 53372000211252229392, 2981808910524462942720, 177468245487057424475136
Offset: 0
-
a(n) = sum(k=0, n\2, (2*k)!*(n+k+1)^(k-1)*abs(stirling(n, 2*k, 1))/k!);
A357092
E.g.f. satisfies A(x)^A(x) = (1 - x * A(x))^log(1 - x * A(x)).
Original entry on oeis.org
1, 0, 2, 6, 58, 580, 7568, 119448, 2195772, 46413792, 1106667072, 29403619080, 861570383232, 27600893313552, 959793100481616, 36006430081497120, 1449539553826089360, 62334045415459189248, 2851721291051846833152, 138299011223141244621024
Offset: 0
-
a(n) = sum(k=0, n\2, (2*k)!*(n-k+1)^(k-1)*abs(stirling(n, 2*k, 1))/k!);
Showing 1-4 of 4 results.