A309509
G.f. satisfies A(A(x)) = F(x), where F(x) is the g.f. for A001787(n) = n*2^(n-1).
Original entry on oeis.org
0, 1, 2, 2, 2, 2, 0, 4, 6, -58, 100, 1052, -5924, -21972, 322020, 332392, -21168682, 29068598, 1724404180, -7070346036, -172304798980, 1290100381724, 20728501384592, -247269172883976, -2936888518668676, 53037176259027580, 477640220538178184
Offset: 0
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half[q_] := half[q] = Module[{h}, h[0] = 0; h[1] = 1; h[n_Integer] := h[n] = Module[{c}, c[m_Integer /; m < n] := h[m]; c[n] /. Solve[q[n] == Sum[k! c[k] BellY[n, k, Table[m! c[m], {m, n - k + 1}]], {k, n}]/n!, c[n]][[1]]]; h]; a[n_Integer] := a[n] = half[Function[k, k 2^(k-1)]][n]; Table[a[n], {n, 0, 26}]
A030275
Denominators of sequence {b(1), b(2),...} which when COMPOSED with itself gives {1,2,3,...}.
Original entry on oeis.org
1, 1, 2, 4, 8, 1, 16, 64, 128, 128, 256, 512, 1024, 2048, 2048, 16384, 32768, 32768, 65536, 131072, 262144, 131072, 524288, 2097152, 4194304, 4194304, 8388608, 2097152, 16777216, 134217728, 67108864, 1073741824, 2147483648, 2147483648, 4294967296, 8589934592
Offset: 1
[ 1, 1, 1/2, 1/4, 1/8, 0, 1/16, 3/64, -29/128, 25/128, 263/256, -1481/512, -5493/1024, 80505/2048 ]
A091138
E.g.f. A(x) satisfies A(A(x)) = x/(1-x)^2.
Original entry on oeis.org
1, 2, 3, 6, 15, 0, 315, 1890, -82215, 708750, 41008275, -1385549550, -33403344975, 3426898600125, 26529571443375, -13516476003780750, 157765729690193625, 84230651703487038750, -3280917943856839411125, -799561865724400084556250, 62859004972802312944044375
Offset: 1
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t[n_, m_] := t[n, m] = If[n == m, 1, 1/2*(Binomial[n+m-1, 2*m-1] - Sum[t[n, i]*t[i, m], {i, m+1, n-1}])]; a[n_] := n!*t[n, 1]; Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Feb 26 2013, after Vladimir Kruchinin *)
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T(n,m):=if n=m then 1 else 1/2*(binomial(n+m-1,2*m-1)-sum(T(n,i)*T(i,m),i,m+1,n-1));
makelist(2^(n-1)*T(n,1),n,1,10); /* Vladimir Kruchinin, Mar 14 2012 */
A334283
Numerators of power series coefficients of A(x) satisfying A(A(x)) = x + Sum_{k>=2} prime(k-1) * x^k.
Original entry on oeis.org
1, 1, 1, 3, -3, 11, -47, 291, -361, -327, 2651, 8117, -23761, -920509, 3401813, 48080231, -949833905, -533061737, 47194458351, 9309105461, -5717668358773, 5794759242411, 416358013987311, -3775846647202969, -144292064358491357, 269618719159718919, 14658236743430975341
Offset: 1
1, 1, 1/2, 3/4, -3/8, 11/8, -47/16, 291/64, -361/128, -327/64, 2651/256, 8117/512, -23761/1024, -920509/2048, ...
Showing 1-4 of 4 results.
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