A371042
E.g.f. satisfies A(x) = 1 + x^2*exp(x*A(x)).
Original entry on oeis.org
1, 0, 2, 6, 12, 140, 1470, 10122, 114296, 1874952, 25462170, 379431470, 7546461252, 151797222876, 3066316693622, 72101615826450, 1843378516587120, 47860832586054032, 1338908395558366386, 40675047500003794902, 1282380661224172506620
Offset: 0
-
nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^3]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *)
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a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(n-2*k+1, k)/((n-2*k+1)*(n-2*k)!));
A371045
E.g.f. satisfies A(x) = 1 + x^3*A(x)*exp(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 840, 15330, 161616, 1572984, 29031120, 636008670, 11426850600, 210095235636, 5137568918664, 139255673359530, 3574532174656800, 95923063388359920, 2974073508961556256, 98747639807081454774, 3287535337205171488440
Offset: 0
A371046
E.g.f. satisfies A(x) = 1 + x^3*A(x)^2*exp(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 1560, 25410, 242256, 3508344, 85882320, 1724406750, 32784999720, 839182482996, 24162605028744, 659439484706730, 19415319297457440, 658935736181053680, 23245444335085544736, 835819877947421773494, 32462532011236141677240
Offset: 0
A371066
E.g.f. satisfies A(x) = 1 + x^3/6*exp(x*A(x)).
Original entry on oeis.org
1, 0, 0, 1, 4, 10, 20, 175, 2296, 20244, 134520, 1016565, 13527580, 209970046, 2785823404, 33569936855, 467250784560, 8358652382760, 159820481883696, 2888819281378089, 51781860691882740, 1031576680142770930, 23237341150372569220, 543570375735294712651
Offset: 0
-
nmax = 20; CoefficientList[Series[1 - ProductLog[-E^x*x^4/6]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *)
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a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-3*k+1, k)/(6^k*(n-3*k+1)*(n-3*k)!));
Showing 1-4 of 4 results.