A360601
E.g.f. satisfies A(x) = exp(x*A(x)^2) / (1-x).
Original entry on oeis.org
1, 2, 13, 166, 3265, 87306, 2957509, 121400350, 5857287937, 324884241874, 20370279663901, 1424790170536470, 109990236302275201, 9289460282062082266, 852049115732672006101, 84345608594930495005966, 8962937531710834906989313, 1017655033307013508626619554
Offset: 0
A370876
Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^3)) ).
Original entry on oeis.org
1, 1, 2, 12, 120, 1320, 17640, 304920, 6249600, 143579520, 3711052800, 107762054400, 3455138332800, 120802387305600, 4583177081683200, 187766031131078400, 8256125218115174400, 387662886088250572800, 19364540503274942976000, 1025507260911983244595200
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^3)))/x))
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a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(n, 3*k)/k!);
A380724
E.g.f. A(x) satisfies A(x) = exp(x * A(x)^3) / (1 - x*A(x)^3).
Original entry on oeis.org
1, 2, 29, 862, 39461, 2454296, 193406953, 18475039808, 2075062993865, 268013104242688, 39139481641977461, 6377306725457207552, 1147019426037344539501, 225728971809041691392000, 48248339461852786811399489, 11131014193619108036340637696, 2756799306857952163745291500433
Offset: 0
A371041
E.g.f. satisfies A(x) = exp(x^2*A(x)^3) / (1-x).
Original entry on oeis.org
1, 1, 4, 30, 348, 5460, 108480, 2609040, 73713360, 2393087760, 87791891040, 3591843726240, 162157925160000, 8007919490450880, 429418816003457280, 24849579630222547200, 1543505958412498080000, 102430107277414595078400, 7232759636684706937612800
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(-3*x^2/(1-x)^3)/(-3*x^2))^(1/3)))
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a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*binomial(n+k, n-2*k)/k!);
Showing 1-4 of 4 results.