A386831 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(4*n+1,k) * binomial(4*n-k,n-k).
1, 23, 814, 32102, 1330436, 56734023, 2464566064, 108464237352, 4819668737436, 215760575713148, 9716002818365314, 439628651114930102, 19971546503835844436, 910318041046245082898, 41611957337801849102064, 1906855257451887625497852, 87569968895543824193201436
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(4*n+1, k)*binomial(4*n-k, n-k));
Formula
a(n) = [x^n] (1+3*x)^(4*n+1)/(1-2*x)^(3*n+1).
a(n) = [x^n] 1/((1-3*x) * (1-5*x)^(3*n+1)).
a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(4*n+1,k).
a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(3*n+k,k).