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 A362478 E.g.f. satisfies A(x) = exp(x + x^3/3 * A(x)^3). 6
 1, 1, 1, 3, 33, 321, 2841, 31641, 498849, 8979489, 167510961, 3427780401, 80374833441, 2089382321313, 58020408889353, 1721768971537161, 55150870311938241, 1897482353016075201, 69322763655015214689, 2676706914491568918369 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..399 Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA E.g.f.: exp(x - LambertW(-x^3 * exp(3*x))/3) = ( -LambertW(-x^3 * exp(3*x))/x^3 )^(1/3). a(n) = n! * Sum_{k=0..floor(n/3)} (1/3)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!). MATHEMATICA nmax = 20; A[_] = 1; Do[A[x_] = Exp[x + x^3/3*A[x]^3] + O[x]^(nmax+1) // Normal, {nmax}]; CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *) PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3*exp(3*x))/3))) CROSSREFS Column k=2 of A362490. Cf. A362474, A362491. Cf. A362390. Sequence in context: A226508 A097486 A121515 * A221883 A002277 A332087 Adjacent sequences: A362475 A362476 A362477 * A362479 A362480 A362481 KEYWORD nonn AUTHOR Seiichi Manyama, Apr 21 2023 STATUS approved

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Last modified August 7 17:47 EDT 2024. Contains 375017 sequences. (Running on oeis4.)