A378327
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k) / ((n-1)*k + 1).
Original entry on oeis.org
1, 2, 5, 25, 257, 4361, 104425, 3241316, 123865313, 5628753361, 296671566941, 17798975341467, 1197924420178381, 89394126594968755, 7326377073291002147, 654215578855903951141, 63225054646397348577601, 6575059243843086616460321, 732138834180570978286488133
Offset: 0
-
Table[Sum[Binomial[n, k] Binomial[n*k, k]/((n-1)*k + 1), {k, 0, n}], {n, 0, 20}]
A378325
G.f. A(x) = Sum_{n>=0} a(n)*x^n, where a(n) = Sum_{k=0..n-1} [x^k] A(x)^k for n >= 1 with a(0) = 1.
Original entry on oeis.org
1, 1, 2, 7, 41, 338, 3499, 42969, 606351, 9633640, 169888025, 3290314970, 69409429043, 1584105116525, 38894316619948, 1022411500472240, 28653072049382809, 852911635849385778, 26876978490909421289, 893929164892155754432, 31296785296935394097351, 1150551256823546563078988
Offset: 0
-
{a(n) = my(A=[1]); for(m=1, n, A=concat(A, 0);
A[#A] = 1 + sum(k=1, m-1, (polcoeff(Ser(A)^k, k)) )); A[n+1]}
for(n=0, 30, print1(a(n), ", ")) \\ after Paul D. Hanna
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}]
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.