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A367373
Expansion of the e.g.f. (exp(x) / (4 - 3*exp(x)))^(3/4).
1
1, 3, 18, 171, 2223, 36648, 731763, 17157591, 461975868, 14045606613, 475876343583, 17777773950786, 725954222357613, 32168297036885103, 1537272547959690378, 78808327981017731631, 4314090689274124348083, 251157836896565547250368
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (k/n - 4) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 3*a(n-1) + 3*Sum_{k=1..n-1} binomial(n-1,k) * a(n-k).
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*prod(j=0, k-1, 4*j+3)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 15 2023
STATUS
approved