A052755
G.f. A(x) satisfies: A(x) = exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^3 * x^k / k ).
Original entry on oeis.org
1, 1, 3, 15, 79, 466, 2872, 18409, 121197, 815491, 5581214, 38737651, 272012178, 1928939678, 13794498614, 99371002295, 720411445866, 5252194141946, 38482834469488, 283223825607253, 2092829973445703
Offset: 0
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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spec := [S,{S=PowerSet(B),B=Prod(S,S,S,Z)},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
-
spec := [S,{S=PowerSet(B),B=Prod(Z,S,S,S,S,S)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
A363468
G.f. A(x) satisfies: A(x) = x + x^2 * exp( Sum_{k>=1} (-1)^(k+1) * A(x^k)^4 / (k*x^(3*k)) ).
Original entry on oeis.org
1, 1, 1, 4, 14, 48, 201, 812, 3455, 14961, 65954, 294884, 1334526, 6098879, 28114885, 130561444, 610244889, 2868547475, 13552299256, 64316483918, 306473091394, 1465727378317, 7033293786125, 33851816310445, 163384902125185, 790589562321385, 3834540111072545, 18638976010097900
Offset: 1
-
nmax = 28; A[] = 0; Do[A[x] = x + x^2 Exp[Sum[(-1)^(k + 1) A[x^k]^4/(k x^(3 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[f[k] f[n - k], {k, 1, n - 1}]; a[n_] := a[n] = (1/(n - 2)) Sum[Sum[(-1)^(k/d + 1)d g[d + 3], {d, Divisors[k]}] a[n - k], {k, 1, n - 2}]; Table[a[n], {n, 1, 28}]
Showing 1-3 of 3 results.
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