A386836
a(n) = Sum_{k=0..n} binomial(3*n+2,k) * binomial(3*n-k-1,n-k).
Original entry on oeis.org
1, 7, 70, 782, 9199, 111465, 1376764, 17234600, 217891693, 2775766091, 35574777154, 458169648722, 5924747347835, 76876586813629, 1000418599504408, 13051488907037580, 170643358430006553, 2235400439909584575, 29333436132847784062, 385507257723471794774, 5073372058467119928391
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+2, k)*binomial(3*n-k-1, n-k));
A386837
a(n) = Sum_{k=0..n} binomial(4*n+2,k) * binomial(4*n-k-1,n-k).
Original entry on oeis.org
1, 9, 126, 1978, 32703, 556887, 9665476, 170006256, 3019802253, 54047520709, 973141183002, 17607177876438, 319855973830251, 5830329608105763, 106583422441886592, 1953315343946213804, 35875864591309216089, 660185366847433991025, 12169379986275311820790
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*n+2, k)*binomial(4*n-k-1, n-k));
A386865
a(n) = Sum_{k=0..n} 2^(n-k) * binomial(2*n+2,k) * binomial(2*n-k-1,n-k).
Original entry on oeis.org
1, 6, 51, 496, 5130, 54894, 600103, 6657312, 74646702, 843819580, 9599776494, 109776491664, 1260666279964, 14528980409454, 167951183468655, 1946529575164864, 22611104963042646, 263175370423429428, 3068541416792813338, 35834296592951011680, 419059482092284948908
Offset: 0
-
Table[Sum[(-1)^k*(k+1)*(k+2)*2^(k-1)*3^(n-k)* Binomial[2*n+2, n+k+2], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 06 2025 *)
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a(n) = sum(k=0, n, 2^(n-k)*binomial(2*n+2, k)*binomial(2*n-k-1, n-k));
Showing 1-3 of 3 results.