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A377828
E.g.f. satisfies A(x) = (1 + x)^3 * exp(x * A(x)).
4
1, 4, 21, 193, 2669, 48711, 1113325, 30615019, 984983193, 36319515355, 1510538562641, 69968975169567, 3572684914283941, 199389519518767111, 12075888110164192917, 788850329621989132771, 55289606764547108653361, 4138807268239824817387443, 329564746571982961088975257
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: (1+x)^3 * exp( -LambertW(-x*(1+x)^3) ).
E.g.f.: -LambertW(-x*(1+x)^3)/x.
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(3*k+3,n-k)/k!.
PROG
(PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+3, n-k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 09 2024
STATUS
approved