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A367963
a(n) = Sum_{j=0..n} (2*n)! / (n!*(n - j)!).
3
1, 4, 30, 320, 4550, 82152, 1808268, 47018400, 1410564870, 47959254200, 1822451844356, 76542978168384, 3520976998449820, 176048849932891600, 9506637896416263000, 551384997992298371520, 34185869875523100114630, 2256267411784526941171800, 157938718824916894957161300
OFFSET
0,2
FORMULA
a(n) = (exp(1) * Gamma(n + 1, 1) * Gamma(2*n + 1)) / Gamma(n + 1)^2.
a(n) * n! = A367962(2*n, n).
MAPLE
a := n -> add((2*n)!/(n!*(n-j)!), j = 0..n):
seq(a(n), n = 0..18);
MATHEMATICA
Table[Sum[(2n)!/(n!(n-j)!), {j, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Feb 10 2024 *)
CROSSREFS
Cf. A367962.
Sequence in context: A360766 A298244 A293191 * A180623 A128329 A211828
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 06 2023
STATUS
approved