A386829 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(2*n+1,k) * binomial(2*n-k,n-k).
1, 13, 204, 3457, 61006, 1103598, 20299434, 377871297, 7097430726, 134243202358, 2553356761264, 48788507855562, 935791802540596, 18007015501848568, 347459946354962694, 6720599552926105377, 130263082422599127366, 2529516572366126192478
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(2*n+1, k)*binomial(2*n-k, n-k));
Formula
a(n) = [x^n] (1+3*x)^(2*n+1)/(1-2*x)^(n+1).
a(n) = [x^n] 1/((1-3*x) * (1-5*x)^(n+1)).
a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(2*n+1,k).
a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(n+k,k).