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A371269
E.g.f. satisfies A(x) = 1 + x*A(x) * (exp(x*A(x)^2) - 1).
3
1, 0, 2, 3, 76, 485, 10746, 146167, 3552312, 75642345, 2150551990, 61400333291, 2061654862356, 72804918721405, 2858153637295698, 119363732105632575, 5395737275060765296, 259270058379207421649, 13294348104095211012462, 721446934706871966578899
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (2*n-k)! * Stirling2(n-k,k)/( (n-k)! * (2*n-2*k+1)! ).
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (2*n-k)!*stirling(n-k, k, 2)/((n-k)!*(2*n-2*k+1)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 16 2024
STATUS
approved