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!));
A357095
E.g.f. satisfies A(x)^A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 / 6).
Original entry on oeis.org
1, 0, 0, 1, 6, 35, 275, 2884, 35672, 494724, 7673670, 132896676, 2544253426, 53252983992, 1208888367596, 29592833903424, 777311220788320, 21808542026480120, 650880782773059840, 20590135175285212800, 688212821908314587880, 24235789570607605377680
Offset: 0
-
a(n) = sum(k=0, n\3, (3*k)!*(n-k+1)^(k-1)*abs(stirling(n, 3*k, 1))/(6^k*k!));
Showing 1-3 of 3 results.