A365782 Expansion of e.g.f. 1 / (3 - 2 * exp(2*x))^(1/4).
1, 1, 7, 79, 1273, 26761, 694207, 21426679, 766897873, 31228168561, 1425551226007, 72103869999679, 4002503339419273, 241916116809963961, 15814645240322565007, 1111830805751346135079, 83649120614618202845473, 6705916845517938558372961
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n, 2^(n-k)*prod(j=0, k-1, 4*j+1)*stirling(n, k, 2));
Formula
a(n) = Sum_{k=0..n} 2^(n-k) * (Product_{j=0..k-1} (4*j+1)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} 2^k * (2 - 3/2 * k/n) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = a(n-1) - 3*Sum_{k=1..n-1} (-2)^k * binomial(n-1,k) * a(n-k).