cp's OEIS Frontend

A386836 a(n) = Sum_{k=0..n} binomial(3*n+2,k) * binomial(3*n-k-1,n-k).

%I A386836 #9 Aug 05 2025 10:01:46
%S A386836 1,7,70,782,9199,111465,1376764,17234600,217891693,2775766091,
%T A386836 35574777154,458169648722,5924747347835,76876586813629,
%U A386836 1000418599504408,13051488907037580,170643358430006553,2235400439909584575,29333436132847784062,385507257723471794774,5073372058467119928391
%N A386836 a(n) = Sum_{k=0..n} binomial(3*n+2,k) * binomial(3*n-k-1,n-k).
%F A386836 a(n) = [x^n] (1+x)^(3*n+2)/(1-x)^(2*n).
%F A386836 a(n) = [x^n] 1/((1-x)^3 * (1-2*x)^(2*n)).
%F A386836 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(3*n+2,k) * binomial(n-k+2,n-k).
%F A386836 a(n) = Sum_{k=0..n} 2^k * binomial(2*n+k-1,k) * binomial(n-k+2,n-k).
%o A386836 (PARI) a(n) = sum(k=0, n, binomial(3*n+2, k)*binomial(3*n-k-1, n-k));
%Y A386836 Cf. A386835, A386837.
%Y A386836 Cf. A370097, A386833.
%K A386836 nonn
%O A386836 0,2
%A A386836 _Seiichi Manyama_, Aug 05 2025