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A361617
a(n) = n! * Sum_{k=0..n} binomial(n+(n-1)*(k+1),n-k)/k!.
2
1, 2, 15, 214, 4721, 146046, 5958367, 307382090, 19459587009, 1478414285146, 132440451881231, 13787717744245182, 1647673524863409265, 223671725058601427414, 34184743554559413628191, 5837132027535188545269106, 1106136052471647285563082497
OFFSET
0,2
LINKS
FORMULA
a(n) = n! * [x^n] exp( x/(1-x)^n ) / (1-x)^n.
a(n) = Sum_{k=0..n} (n+(n-1)*(k+1))!/(n*k+n-1)! * binomial(n,k) for n > 0.
PROG
(PARI) a(n) = n!*sum(k=0, n, binomial(n+(n-1)*(k+1), n-k)/k!);
CROSSREFS
Main diagonal of A361616.
Cf. A361607.
Sequence in context: A143881 A377890 A298692 * A132493 A135860 A378041
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2023
STATUS
approved