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A378043
E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x) * A(x)^2 ).
2
1, 2, 13, 190, 4045, 116746, 4251289, 187255174, 9684799961, 575477786674, 38638577549701, 2893159369162030, 239045577899472997, 21604942464613062010, 2120362938300115706513, 224568728344893756230326, 25529660577970226603535793, 3100816199696659908092912866
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: (1+x) * exp( -LambertW(-2*x*(1+x)^3)/2 ).
a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(3*k+1,n-k)/k!.
PROG
(PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(3*k+1, n-k)/k!);
CROSSREFS
Cf. A377894.
Sequence in context: A378093 A226865 A062156 * A371318 A323209 A239994
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 15 2024
STATUS
approved