A354413
Expansion of e.g.f. 1/(2 - exp(x))^x.
Original entry on oeis.org
1, 0, 2, 6, 36, 250, 2100, 20594, 231168, 2923722, 41149140, 637972522, 10804678632, 198480649250, 3930963078588, 83500876635570, 1893745346613216, 45672635292831322, 1167233799092342148, 31510575263852229242, 896028017040096045720
Offset: 0
-
With[{nn=20},CoefficientList[Series[1/(2-Exp[x])^x,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 03 2025 *)
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x))^x))
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, (k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;
A354083
Expansion of e.g.f. (1 + log(1-x))^x.
Original entry on oeis.org
1, 0, -2, -6, -16, -55, -288, -2128, -19808, -219546, -2816530, -41002236, -666782136, -11961352104, -234327748900, -4972665181170, -113552835539328, -2774993356571920, -72238332282154344, -1995222148760626392, -58268719729725843880, -1793842001139571701696
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace((1+log(1-x))^x))
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, j*sum(k=1, j-1, (k-1)!*abs(stirling(j-1, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;
A354416
Expansion of e.g.f. (1 - log(1-x))^x.
Original entry on oeis.org
1, 0, 2, 0, 16, 5, 288, 392, 9840, 33462, 582910, 3652044, 55557192, 524095728, 7910319116, 98390834310, 1573086910848, 23774700449584, 414180226506456, 7249907657342184, 138771378745878680, 2735366111451910944, 57469663931297252976, 1253755421949789141624
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace((1-log(1-x))^x))
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^j*j*sum(k=1, j-1, (k-1)!*stirling(j-1, k, 1))*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-3 of 3 results.