A378327 - OEIS

%I #9 Nov 23 2024 12:46:50

%S 1,2,5,25,257,4361,104425,3241316,123865313,5628753361,296671566941,

%T 17798975341467,1197924420178381,89394126594968755,

%U 7326377073291002147,654215578855903951141,63225054646397348577601,6575059243843086616460321,732138834180570978286488133

%N a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n*k,k) / ((n-1)*k + 1).

%H Vaclav Kotesovec, <a href="/A378327/b378327.txt">Table of n, a(n) for n = 0..338</a>

%F a(n) ~ exp(n + exp(-1) - 1/2) * n^(n - 5/2) / sqrt(2*Pi).

%t Table[Sum[Binomial[n, k] Binomial[n*k, k]/((n-1)*k + 1), {k, 0, n}], {n, 0, 20}]

%Y Cf. A007317, A007556, A188687, A346646, A346647, A346648, A346649, A346650.

%Y Cf. A378326.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Nov 23 2024