A371039
E.g.f. satisfies A(x) = exp(x^3*A(x)) / (1-x).
Original entry on oeis.org
1, 1, 2, 12, 72, 480, 4680, 52920, 645120, 9313920, 153014400, 2720995200, 53428636800, 1154333980800, 26847281260800, 671610658118400, 18064388076134400, 517898679679180800, 15763026427487539200, 508612525689235968000, 17329554246181072896000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(-x^3/(1-x))/(-x^3)))
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a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n-2*k, n-3*k)/k!);
A378090
E.g.f. satisfies A(x) = exp(x * (1-x)^2 * A(x)) / (1-x)^3.
Original entry on oeis.org
1, 4, 23, 181, 1889, 25411, 427615, 8736337, 210911489, 5882285971, 186121646831, 6585885144697, 257640988064641, 11039620794801691, 514147575711741119, 25858553659455655201, 1396703647943164718081, 80633376290492591578147, 4954794080385073122030799
Offset: 0
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terms = 19; A[] = 0; Do[A[x] = Exp[x*(1-x)^2*A[x]]/(1-x)^3 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Mar 24 2025 *)
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a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2, n-k)/k!);
A378091
E.g.f. satisfies A(x) = exp(x * (1-x)^3 * A(x)) / (1-x)^4.
Original entry on oeis.org
1, 5, 33, 280, 3009, 40456, 670351, 13428794, 318341841, 8747362540, 273595272231, 9595433139238, 372786185735497, 15885841209363152, 736549352642825247, 36906793949098033906, 1987212351128733260577, 114415986259681057007956, 7014281833059332148174007
Offset: 0
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terms = 19; A[] = 0; Do[A[x] = Exp[x*(1-x)^3*A[x]]/(1-x)^4 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Mar 24 2025 *)
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a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+3, n-k)/k!);
A378092
E.g.f. satisfies A(x) = exp( x * (1-x) * A(x)^2 ) / (1-x).
Original entry on oeis.org
1, 2, 11, 118, 1993, 46386, 1376059, 49601014, 2104366513, 102717184546, 5670357524011, 349304240222070, 23754501885783673, 1767641331001915474, 142868173684094891803, 12463599550013379095926, 1167281368458948415748833, 116814664082977998388994370, 12440156205235958837516345419
Offset: 0
A378093
E.g.f. satisfies A(x) = exp( x * (1-x)^2 * A(x)^3 ) / (1-x).
Original entry on oeis.org
1, 2, 13, 187, 4421, 145381, 6106885, 312010217, 18775791529, 1300609323577, 101932831136801, 8917429459192717, 861423205666601869, 91071085791088039781, 10459294205668851438589, 1296711971347861868098561, 172604468588739615868724945, 24551969347625035312300681969
Offset: 0
A378094
E.g.f. satisfies A(x) = exp( x^2 * A(x) / (1-x) ) / (1-x).
Original entry on oeis.org
1, 1, 4, 24, 204, 2220, 29640, 469560, 8623440, 180306000, 4231815840, 110217270240, 3155551439040, 98529432281280, 3332752472649600, 121416875166787200, 4740431035737196800, 197475789694088505600, 8743499113411321459200, 410050296758706725721600
Offset: 0
A378095
E.g.f. satisfies A(x) = exp( x^3 * A(x) / (1-x)^2 ) / (1-x).
Original entry on oeis.org
1, 1, 2, 12, 120, 1320, 16200, 234360, 3991680, 77535360, 1678924800, 40142995200, 1053264643200, 30109980700800, 931249403884800, 30979797430982400, 1103292884684390400, 41889177988142284800, 1689202127352118579200, 72105273328152166502400
Offset: 0