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, ...
A334284
Denominators 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, 2, 4, 8, 8, 16, 64, 128, 64, 256, 512, 1024, 2048, 2048, 16384, 32768, 16384, 65536, 131072, 262144, 262144, 524288, 2097152, 4194304, 2097152, 8388608, 8388608, 16777216, 134217728, 67108864, 1073741824, 2147483648, 1073741824, 4294967296
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, ...
A316186
Expansion of e.g.f. P(P(x)), where P(x) = Sum_{k>=1} prime(k)*x^k/k!.
Original entry on oeis.org
4, 18, 104, 687, 5064, 40934, 358083, 3346832, 33123000, 345219919, 3777134694, 43291666298, 518855171115, 6491738816768, 84656365477452, 1148895613585775, 16201725990730392, 237030534528945348, 3591398122456079285, 56254812062478841340, 909319044063443870702
Offset: 1
E.g.f.: A(x) = 4*x + 18*x^2/2! + 104*x^3/3! + 687*x^4/4! + 5064*x^5/5! + 40934*x^6/6! + ...
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p[x_] := p[x] = Sum[Prime[k] x^k/k!, {k, 21}]; a[n_] := a[n] = SeriesCoefficient[p[p[x]], {x, 0, n}]; Table[n! a[n], {n, 21}]
Showing 1-3 of 3 results.
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