A367835
Expansion of e.g.f. 1/(2 - x - exp(2*x)).
Original entry on oeis.org
1, 3, 22, 242, 3544, 64872, 1424976, 36517840, 1069533824, 35240047232, 1290137297152, 51955085596416, 2282489348834304, 108630445541684224, 5567741266098944000, 305752314499878569984, 17909736027185859100672, 1114647522476340562132992
Offset: 0
-
A367835 := proc(n)
option remember ;
if n = 0 then
1 ;
else
n*procname(n-1)+add(2^k*binomial(n,k)*procname(n-k),k=1..n) ;
end if;
end proc:
seq(A367835(n),n=0..70) ; # R. J. Mathar, Dec 04 2023
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;
A367846
Expansion of e.g.f. 1/(1 - x + log(1 - 3*x)).
Original entry on oeis.org
1, 4, 41, 654, 14028, 377112, 12177126, 458916588, 19769059944, 958125646080, 51597765220608, 3056601306206016, 197532472461453072, 13829353660386169344, 1042679226974498229456, 84229294995413626072608, 7257792124889497549663488
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 3^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
A367837
Expansion of e.g.f. 1/(2 - x - exp(4*x)).
Original entry on oeis.org
1, 5, 66, 1294, 33752, 1100504, 43060176, 1965653232, 102548623744, 6018735869824, 392498702352128, 28155539333730560, 2203322337542003712, 186790304541786160128, 17053569926181643921408, 1668166923908523824576512, 174057374767036007615922176
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 4^j*binomial(i, j)*v[i-j+1])); v;
A367831
E.g.f. A(x) satisfies A(x) = (1 + (exp(x) - 1) * A(3*x)) / (1 - x).
Original entry on oeis.org
1, 2, 17, 529, 60191, 24822701, 36413854321, 186201636968159, 3260017071214457747, 192544750449664642891369, 37901471231124512743264725077, 24619109083914012570141331273785011, 52334858943702505364559907161989713988743
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 3^(i-j)*binomial(i, j)*v[i-j+1])); v;
A367839
Expansion of e.g.f. 1/(2 + x - exp(3*x)).
Original entry on oeis.org
1, 2, 17, 183, 2679, 48903, 1071621, 27394965, 800378019, 26307021483, 960739737777, 38595129840369, 1691405818822719, 80301792637126791, 4105701241574252445, 224912022483008478141, 13142159127790633537947, 815924005186398537216483
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-i*v[i]+sum(j=1, i, 3^j*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
-
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;
Showing 1-6 of 6 results.