A238085
Expansion of e.g.f.: -LambertW(-sinh(x)).
Original entry on oeis.org
0, 1, 2, 10, 72, 716, 9088, 140344, 2554240, 53540368, 1270296064, 33653698464, 984753299456, 31542901202112, 1097763264864256, 41247391653500800, 1664188908529156096, 71759140177774010624, 3293251384307726942208, 160272893566770148403712
Offset: 0
-
CoefficientList[Series[-LambertW[-Sinh[x]],{x,0,20}],x]*Range[0,20]!
-
x='x+('x^30); concat([0], Vec(serlaplace(-lambertw(-sinh(x))))) \\ G. C. Greubel, Feb 19 2018
A385425
Expansion of e.g.f. exp( -LambertW(-arcsinh(x)) ).
Original entry on oeis.org
1, 1, 3, 15, 113, 1145, 14499, 220703, 3932865, 80342577, 1851286755, 47510525007, 1344106404849, 41562628517865, 1394711974335939, 50480840239135455, 1960392617938419969, 81309789407316485217, 3587373056789171999811, 167762667997938465311247
Offset: 0
A381147
E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)) / A(x) ).
Original entry on oeis.org
1, 1, 1, 2, 13, 92, 621, 5112, 56057, 705168, 9480665, 141039648, 2366242693, 43609330624, 864164283269, 18414385180544, 422574196387953, 10374625080684800, 270563138370828465, 7472794772378583552, 218190569313134267517, 6714970997524417977344
Offset: 0
-
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (n-k+1)^(k-1)*a136630(n, k));
A381262
Expansion of e.g.f. exp( -LambertW(-2 * sinh(x)) / 2 ).
Original entry on oeis.org
1, 1, 5, 50, 749, 15132, 385953, 11907520, 431376345, 17954558928, 844397935517, 44287052219104, 2563077440429701, 162259043437047104, 11154216390820950585, 827464985582299977728, 65889383717510410496689, 5605511011776107945980160, 507429545895353798767136181
Offset: 0
-
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (2*k+1)^(k-1)*a136630(n, k));
Showing 1-4 of 4 results.