OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (4 - k/n) * binomial(n,k) * a(n-k).
a(n) ~ Gamma(1/4) * n^(n + 1/4) / (5^(3/4) * sqrt(Pi) * exp(n) * log(5/4)^(n + 3/4)). - Vaclav Kotesovec, Nov 11 2023
a(0) = 1; a(n) = 3*a(n-1) - 5*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Nov 16 2023
MATHEMATICA
a[n_] := Sum[Product[4*j + 3, {j, 0, k - 1}] * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 11 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 4*j+3)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 09 2023
STATUS
approved