A371044
E.g.f. satisfies A(x) = 1 + x^3*exp(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 120, 5250, 80976, 726264, 4839120, 86487390, 2283242280, 42585905076, 590667519624, 10115535833130, 286758920451360, 8128299117822960, 186279550983756576, 4123388294626654134, 118916807955913504440, 4102548791571529697580
Offset: 0
-
nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^4]/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)/((n-3*k+1)*(n-3*k)!));
A371043
E.g.f. satisfies A(x) = 1 + x^2*A(x)*exp(x*A(x)).
Original entry on oeis.org
1, 0, 2, 6, 36, 380, 3630, 47082, 725816, 12132360, 235801530, 5083309550, 119757623172, 3103443520476, 87082536196838, 2632399338834930, 85471932351187440, 2961803643600574352, 109154615479427298546, 4264407640037365789014, 175984871341042826680700
Offset: 0
A371063
E.g.f. satisfies A(x) = 1 + x^2/2*exp(x*A(x)).
Original entry on oeis.org
1, 0, 1, 3, 6, 40, 375, 2541, 21028, 264636, 3303765, 41219695, 625493946, 10676900598, 185753808331, 3495429297465, 72963017028840, 1606964677740376, 37107535997019753, 918150959889615771, 24110308315512081550, 662150320109499176130, 19105058680403510485671
Offset: 0
-
nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^3/2]/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)/(2^k*(n-2*k+1)*(n-2*k)!));
Showing 1-3 of 3 results.