Original entry on oeis.org
1, 2, -1, 3, -11, 44, -187, 827, -3751, 17313, -81004, 383390, -1833029, 8843224, -43007753, 210670655, -1038597645, 5149654796, -25664518105, 128493771585, -645988558986, 3259776393676, -16505191207192, 83828620957326, -426961815072785
Offset: 0
-
read("transforms") ;
Lp := [ 0,1,seq(ithprime(i),i=1..25) ] ;
a007296 := REVERT(Lp) ;
a007296x := add( op(i,a007296)*x^i,i=1..nops(a007296)) ;
a187111x := taylor(x/a007296x ,x=0,nops(a007296)+1);
for n from 0 to nops(a007296)-1 do printf("%d,",coeftayl(a187111x,x=0,n)) ; end do; # R. J. Mathar, Mar 29 2011
A334263
E.g.f. A(x) satisfies: A(x) = x - Sum_{k>=2} prime(k-1) * A(x)^k / k!.
Original entry on oeis.org
1, -2, 9, -65, 653, -8432, 133190, -2488589, 53690330, -1313508417, 35929413073, -1086587503799, 35998774583176, -1296581783771904, 50442455219483951, -2108020240791081088, 94179374365406507609, -4479409651990684350045, 225977974437623955594777
Offset: 1
-
nmax = 19; CoefficientList[InverseSeries[Series[x + Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
A291533
Expansion of the series reversion of g.f. for the nonprime numbers (A018252).
Original entry on oeis.org
1, -4, 26, -208, 1859, -17790, 178308, -1847882, 19640154, -212911066, 2345049018, -26168243862, 295214515662, -3361428239216, 38580429168968, -445874925644701, 5184317812361117, -60603410700370525, 711826341810784570, -8396670336877539127, 99428914632341468974
Offset: 1
A366011
G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} prime(k) * A(x)^k.
Original entry on oeis.org
1, -3, 13, -67, 379, -2267, 14065, -89515, 580379, -3815731, 25356051, -169898467, 1145825123, -7767073859, 52858784539, -360823702851, 2468606626813, -16915880702563, 116028193869805, -796200367684945, 5463239318586601, -37465765826805457, 256664142145450777, -1755608165010431139
Offset: 1
-
nmax = 24; A[] = 0; Do[A[x] = x - Sum[Prime[k] A[x]^k, {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
nmax = 24; CoefficientList[InverseSeries[Series[x + Sum[Prime[k] x^k, {k, 2, nmax}], {x, 0, nmax}], x], x] // Rest
Showing 1-4 of 4 results.
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