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 A362774 E.g.f. satisfies A(x) = exp( x * (1+x)^2 * A(x)^2 ). 1
 1, 1, 9, 115, 2265, 59701, 1981513, 79441167, 3736418801, 201790517833, 12309193580841, 837132560820139, 62809405894333321, 5154060532188515325, 459202970647825870313, 44146740571635016905991, 4555272678073789024849377, 502153774773932684443210513 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..17. Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA E.g.f.: exp( -LambertW(-2*x * (1+x)^2)/2 ). a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(2*k,n-k)/k!. MAPLE A362774 := proc(n) n!*add((2*k+1)^(k-1) * binomial(2*k, n-k)/k!, k=0..n) ; end proc: seq(A362774(n), n=0..70) ; # R. J. Mathar, Dec 04 2023 PROG (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*(1+x)^2)/2))) CROSSREFS Cf. A361278, A362772. Cf. A052750, A360547, A362776. Sequence in context: A157551 A157570 A223499 * A157233 A292350 A188976 Adjacent sequences: A362771 A362772 A362773 * A362775 A362776 A362777 KEYWORD nonn AUTHOR Seiichi Manyama, May 02 2023 STATUS approved

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Last modified April 15 13:47 EDT 2024. Contains 371689 sequences. (Running on oeis4.)