A052775
G.f. A(x) satisfies: A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^4 * x^k / k ).
Original entry on oeis.org
1, 1, 4, 26, 184, 1443, 11888, 101859, 897529, 8085103, 74113656, 689134849, 6484074328, 61620879930, 590628242876, 5703027934533, 55423681958153, 541689157201498, 5320989368024126, 52503593913927276
Offset: 0
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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spec := [S,{B=Prod(Z,S,S,S,S),S=PowerSet(B)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
A052798
G.f. A(x) satisfies: A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^5 * x^k / k ).
Original entry on oeis.org
1, 1, 5, 40, 355, 3475, 35836, 384436, 4243860, 47905385, 550404336, 6415528666, 75677788275, 901728156490, 10837196405920, 131215506276862, 1599078373019073, 19598996116313001, 241433496694878595
Offset: 0
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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spec := [S,{S=PowerSet(B),B=Prod(Z,S,S,S,S,S)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
A363467
G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^3 / (k*x^(2*k)) ).
Original entry on oeis.org
1, 1, 1, 3, 9, 25, 88, 292, 1031, 3685, 13433, 49608, 185465, 699963, 2664650, 10217130, 39428179, 153009240, 596761737, 2337875430, 9195732624, 36301739221, 143780858517, 571191310205, 2275409450019, 9087376470138, 36377539265376, 145937953205705, 586645566919856
Offset: 1
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nmax = 29; A[] = 0; Do[A[x] = x + x^2 Exp[Sum[(-1)^(k + 1) A[x^k]^3/(k x^(2 k)), {k, 1, nmax}]] + O[x]^(nmax + 1)//Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
a[1] = a[2] = 1; f[n_] := f[n] = Sum[a[k] a[n - k], {k, 1, n - 1}]; g[n_] := g[n] = Sum[a[k] f[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[(-1)^(k/d + 1) d g[d + 2], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 29}]
Showing 1-3 of 3 results.
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