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A362084
a(n) = Sum_{k=0..n} (-1)^k * binomial(-2,k) * binomial(n*k,n-k).
4
1, 2, 7, 28, 145, 896, 6328, 50212, 441489, 4248370, 44306306, 496991848, 5959111223, 75977511442, 1025441134747, 14594189335496, 218290221112929, 3421314388169988, 56043004143343843, 957209642080023286, 17011439135301438016, 313980693855333453740
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} (k+1) * binomial(n*k,n-k).
a(n) = [x^n] 1/(1 - x*(1+x)^n)^2.
PROG
(PARI) a(n) = sum(k=0, n, (k+1)*binomial(n*k, n-k));
CROSSREFS
Column k=2 of A362079.
Cf. A099237.
Sequence in context: A030946 A030906 A307594 * A296726 A334613 A365559
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 08 2023
STATUS
approved