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A367880
Expansion of e.g.f. 1/(1 - 2 * x * (exp(x) - 1)).
3
1, 0, 4, 6, 104, 490, 7452, 65534, 1062224, 13825746, 252414020, 4303920742, 89701635960, 1870259792570, 44391086228972, 1085906907998670, 29112549152845472, 813723252665063842, 24402507959486170260, 765358519469125339190
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = 2 * n * Sum_{k=2..n} binomial(n-1,k-1) * a(n-k).
a(n) = n! * Sum_{k=0..floor(n/2)} 2^k * k! * Stirling2(n-k,k)/(n-k)!.
PROG
(PARI) a(n) = n!*sum(k=0, n\2, 2^k*k!*stirling(n-k, k, 2)/(n-k)!);
CROSSREFS
Sequence in context: A213128 A105037 A139730 * A013023 A012909 A219507
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 03 2023
STATUS
approved