A362794
E.g.f. satisfies A(x) = (1+x)^(A(x)^x).
Original entry on oeis.org
1, 1, 0, 6, 0, 170, -120, 12446, -35336, 1832400, -12172320, 469680552, -5524990416, 189586178184, -3321122831208, 111608536026360, -2599887499382400, 90253048158627072, -2595580675897337856, 95720854442948910720, -3237436187047116892800
Offset: 0
A362795
E.g.f. satisfies A(x) = (1+x)^(A(x)^(x^2)).
Original entry on oeis.org
1, 1, 0, 0, 24, 0, -60, 7980, -12992, -23184, 10320480, -54616320, 160009344, 33740939232, -391545030240, 3173349947040, 211401523687680, -4586955333880320, 66611949275370240, 2068372502060292864, -82278329345056212480, 1885659676128917982720
Offset: 0
A355780
E.g.f. satisfies A(x) = (1 + x)^(2 * A(x)).
Original entry on oeis.org
1, 2, 10, 96, 1352, 25400, 597816, 16941568, 561993344, 21372060672, 916910785920, 43817650647936, 2308500130055808, 132941831957885184, 8308594453077321984, 560108109905112238080, 40514005700203717945344, 3129925644058623770173440
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*log(1+x)))))
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a(n) = sum(k=0, n, 2^k*(k+1)^(k-1)*stirling(n, k, 1));
A355787
E.g.f. satisfies A(x) = (1 + 2*x)^(A(x)/2).
Original entry on oeis.org
1, 1, 1, 6, 17, 220, 939, 20930, 107393, 3823416, 20382195, 1147905462, 5519388225, 515034742404, 1817577994491, 323878306632330, 481078381979649, 272556878473903344, -355395800536648605, 296393140746445749246, -1420979986049970526335
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-log(1+2*x)/2))))
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a(n) = sum(k=0, n, 2^(n-k)*(k+1)^(k-1)*stirling(n, k, 1));
A214930
E.g.f. satisfies: A(x) = Sum_{n>=0} 1/n! * Product_{k=1..n} log(1 + x*A(x)^k).
Original entry on oeis.org
1, 1, 2, 9, 66, 650, 8250, 127519, 2318876, 48626556, 1154334060, 30589513350, 895415799960, 28693464851688, 999009599484624, 37554576369815400, 1516080931559327280, 65418533528228549744, 3004726893339734134128, 146370356574519380115240
Offset: 0
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 66*x^4/4! + 650*x^5/5! +...
where
A(x) = 1 + log(1+x*A(x)) + log(1+x*A(x))*log(1+x*A(x)^2)/2! + log(1+x*A(x))*log(1+x*A(x)^2)*log(1+x*A(x)^3)/3! + log(1+x*A(x))*log(1+x*A(x)^2)*log(1+x*A(x)^3)*log(1+x*A(x)^4)/4! +...
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{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,prod(k=1,m,log(1+x*A^k+x*O(x^n)))/m!));n!*polcoeff(A,n)}
for(n=0,20,print1(a(n),", "))