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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
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
Sequence in context: A157551 A157570 A223499 * A157233 A292350 A188976
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.)