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A367757
E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3 + x^4) * A(x^5/120)).
3
1, 1, 3, 13, 73, 501, 3337, 27637, 254409, 2557369, 27603631, 313768731, 3905502745, 51573777841, 718307494269, 10507900625251, 161239887204721, 2608009648536417, 43989477103304155, 772109936171046001, 14085074476090366761, 266890182641557777093
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/5)) * a(n-1-k) / (120^floor(k/5) * floor(k/5)! * (n-1-k)!).
PROG
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=0, i-1, (j+1)*v[j\5+1]*v[i-j]/(120^(j\5)*(j\5)!*(i-1-j)!))); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 29 2023
STATUS
approved