A378611 a(n) = Sum_{k=0..n} binomial(2*n+k-1,k) * binomial(n-1,n-k).
1, 2, 14, 104, 806, 6412, 51908, 425476, 3520070, 29332940, 245841284, 2070093632, 17499188924, 148414157816, 1262280506144, 10762045739644, 91951462167110, 787113739061260, 6749009521216052, 57954807274992208, 498334047795436276, 4290199618047230824
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(2*n+k-1, k)*binomial(n-1, n-k));
Formula
a(n) = [x^n] 1/(1 - x/(1 - x))^(2*n).
a(n) = (1/2)^n * [x^(2*n)] 2/(1 - x/(1 - x))^n for n > 0.
a(n) = 2 * A259554(n) for n > 0.