A382859 a(n) = Sum_{k=0..n} binomial(n,k) * binomial((n-1)*(k+1),n-k).
1, 1, 5, 37, 345, 3851, 49468, 713931, 11391985, 198523495, 3741919446, 75702725440, 1633591960883, 37404262517506, 904734768056239, 23030071358784701, 614912094171482849, 17172036245893988575, 500281954849350450946, 15170753984617328108901
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..150
Programs
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Magma
[&+[Binomial(n,k) * Binomial((n-1)*(k+1),n-k): k in [0..n]]: n in [0..21]]; // Vincenzo Librandi, Apr 09 2025
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Mathematica
Table[Sum[Binomial[n,k] * Binomial[(n-1)*(k+1),n-k], {k,0,n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 07 2025 *) -
PARI
a(n) = sum(k=0, n, binomial(n, k)*binomial((n-1)*(k+1), n-k));
Formula
a(n) = [x^n] (1 + x/(1-x)^n)^n.