A385670 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(3*n+1,k) * binomial(3*n-k,n-k).
1, 17, 429, 12048, 355501, 10792737, 333781044, 10457735928, 330823760061, 10543365694707, 338004221112309, 10887987584565108, 352127854740967596, 11426385227977214252, 371844089088280093224, 12130745906826301055088, 396599383187880024765981
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(3*n+1, k)*binomial(3*n-k, n-k));
Formula
a(n) = [x^n] (1+2*x)^(3*n+1)/(1-3*x)^(2*n+1).
a(n) = [x^n] 1/((1-2*x) * (1-5*x)^(2*n+1)).
a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(3*n+1,k).
a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(2*n+k,k).