A378326
a(n) = Sum_{k=0..n} binomial(n-1,k-1) * binomial(n*k,k) / ((n-1)*k+1).
Original entry on oeis.org
1, 1, 3, 19, 219, 3901, 95838, 3022909, 116798643, 5350403737, 283728025998, 17104314563843, 1155635807408096, 86513627563199279, 7109252862969177287, 636268582522962837475, 61610670571434193189443, 6418044336586421956746033, 715718717341021991299583730
Offset: 0
-
Table[Sum[Binomial[n-1, k-1]*Binomial[n*k, k]/((n-1)*k+1), {k, 0, n}], {n, 0, 20}]
A378409
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(n*k,k) / ((n-1)*k+1).
Original entry on oeis.org
1, 0, 1, 5, 73, 1409, 36601, 1198798, 47594289, 2225255777, 119896198381, 7320401163591, 499766786359501, 37739036987427515, 3123975386959740223, 281348109008473891049, 27391364013973766381281, 2866934827195653717595713, 321048532728871544387444869, 38303867032042004479765603315
Offset: 0
-
Table[Sum[(-1)^(n-k) * Binomial[n, k] * Binomial[n*k, k]/((n-1)*k + 1), {k, 0, n}], {n, 0, 20}]
A383120
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k).
Original entry on oeis.org
1, 2, 11, 139, 2885, 82381, 2979565, 130203494, 6664589321, 390857822425, 25832193906761, 1899273577364197, 153741850998047053, 13585520026454056279, 1301210398133681268381, 134270617908678099820891, 14849785991790603714043921, 1752283118795349858851381297
Offset: 0
-
Table[Sum[Binomial[n, k] Binomial[n k, k], {k, 0, n}], {n, 0, 17}]
-
a(n) = sum(k=0, n, binomial(n,k) * binomial(n*k,k)); \\ Michel Marcus, Apr 17 2025
A378410
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,k-1) * binomial(n*k,k) / ((n-1)*k+1).
Original entry on oeis.org
1, 1, 1, 7, 85, 1581, 40006, 1288729, 50578445, 2344950745, 125538581926, 7626452229331, 518557071012696, 39027861427630167, 3221686807607369921, 289464281567009809303, 28124498248184961490621, 2938498159807193630239281, 328556126358414341918608978
Offset: 0
-
Table[Sum[(-1)^(n-k) * Binomial[n-1, k-1] * Binomial[n*k, k]/((n-1)*k + 1), {k, 0, n}], {n, 0, 20}]
Showing 1-4 of 4 results.