A352308
Expansion of e.g.f. 1/(2 - exp(x) - x^4/24).
Original entry on oeis.org
1, 1, 3, 13, 76, 551, 4803, 48833, 567465, 7418263, 107752293, 1721642143, 30008756055, 566650322031, 11523037802461, 251062618129063, 5834798259848815, 144078299659541361, 3766993649599221903, 103961442644871088897, 3020133228180079209075
Offset: 0
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m = 20; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^4/24), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
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my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^4/24)))
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b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m))*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 4);
A032112
"BIJ" (reversible, indistinct, labeled) transform of 2,1,1,1...
Original entry on oeis.org
2, 5, 31, 276, 3111, 42143, 666128, 12033346, 244550149, 5522134317, 137163540306, 3716712490472, 109104171183047, 3449120959632091, 116825788063473052, 4220828797872750510, 162026366682646437513
Offset: 1
A367924
Expansion of e.g.f. 1/(3 - x - 2*exp(x)).
Original entry on oeis.org
1, 3, 20, 200, 2666, 44422, 888214, 20719722, 552385386, 16567346630, 552104425070, 20238679934002, 809341290336274, 35062535546332062, 1635835480858764342, 81770970437144725034, 4360009179878123161658, 247004345719314584973430
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+2*sum(j=1, i, binomial(i, j)*v[i-j+1])); v;
A367925
Expansion of e.g.f. 1/(4 - x - 3*exp(x)).
Original entry on oeis.org
1, 4, 35, 459, 8025, 175383, 4599507, 140728437, 4920898317, 193579534155, 8461200381111, 406815231899409, 21337866382711521, 1212458502624643719, 74193773349948903483, 4864422156647044661949, 340191752483516373189621, 25278147388666498256368323
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+3*sum(j=1, i, binomial(i, j)*v[i-j+1])); v;