A379022
a(n) = Sum_{k=0..n} binomial(2*n+k-1,k) * binomial(2*n+k,n-k).
Original entry on oeis.org
1, 4, 36, 370, 4012, 44824, 510498, 5892310, 68684540, 806715964, 9532070396, 113179713046, 1349276883346, 16140148109960, 193629588953214, 2328744593780590, 28068490664161756, 338960821947139640, 4100329281075440400, 49676100591186493156, 602654837914634224812
Offset: 0
-
a(n) = sum(k=0, n, binomial(2*n+k-1, k)*binomial(2*n+k, n-k));
A379026
a(n) = Sum_{k=0..n} binomial(4*n+k-1,k) * binomial(4*n+k,n-k).
Original entry on oeis.org
1, 8, 136, 2612, 52888, 1103248, 23458756, 505519792, 11001461560, 241240165796, 5321735043496, 117969960106380, 2625673485660100, 58638653062716488, 1313363972969179904, 29489827322243843032, 663600214363813934328, 14961465721142755457484
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*n+k-1, k)*binomial(4*n+k, n-k));
A379086
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n+k,n-2*k).
Original entry on oeis.org
1, 3, 21, 174, 1509, 13443, 121962, 1120899, 10401021, 97230090, 914283621, 8638552464, 81945757734, 779949538176, 7444735446813, 71237074583589, 683125330952205, 6563268117869076, 63164380112090814, 608805362150884731, 5875874727915635409, 56780302474503539427, 549294315060885105744
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(3*n+k-1, k)*binomial(3*n+k, n-2*k));
A379087
a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(3*n+k,n-3*k).
Original entry on oeis.org
1, 3, 15, 93, 651, 4803, 36177, 275208, 2108091, 16243671, 125817345, 978933354, 7646000421, 59915086026, 470820659940, 3708756501018, 29276677544619, 231540519752376, 1834228504348863, 14552075416977531, 115605043235217081, 919503729585453147
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(3*n+k-1, k)*binomial(3*n+k, n-3*k));
A379023
Expansion of (1/x) * Series_Reversion( x * ((1 - x - x^2)/(1 + x))^3 ).
Original entry on oeis.org
1, 6, 57, 653, 8277, 111780, 1576671, 22955298, 342377304, 5204438258, 80334470136, 1255798641861, 19840021268937, 316286673287724, 5081503084814883, 82193597974971157, 1337397202150986387, 21875767255039745856, 359499909751084059372, 5932767953991599086905
Offset: 0
-
a(n) = 3*sum(k=0, n, binomial(3*n+k+3, k)*binomial(3*n+k+3, n-k)/(3*n+k+3));
Showing 1-5 of 5 results.