A355112
Expansion of e.g.f. 4 / (5 - 4*x - exp(4*x)).
Original entry on oeis.org
1, 2, 12, 112, 1376, 21056, 386688, 8286720, 202958848, 5592199168, 171203895296, 5765504860160, 211811563929600, 8429932686999552, 361312700788375552, 16592261047219388416, 812749365813312487424, 42299637489384965537792, 2330989060564353634271232
Offset: 0
-
nmax = 18; CoefficientList[Series[4/(5 - 4 x - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
A343672
a(0) = 1; a(n) = 2 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
Original entry on oeis.org
1, 3, 19, 181, 2299, 36501, 695427, 15457709, 392672651, 11221959685, 356339728243, 12446649786429, 474273933636411, 19577992095770837, 870345573347448803, 41455153171478627533, 2106173029315813515883, 113694251997087087941925, 6498401704686168598548435, 392062852538564346207533789
Offset: 0
-
a[0] = 1; a[n_] := a[n] = 2 n a[n - 1] + Sum[Binomial[n, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[1/(2 (1 - x) - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
A343673
a(0) = 1; a(n) = 3 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
Original entry on oeis.org
1, 4, 33, 409, 6759, 139621, 3460989, 100091335, 3308146179, 123005753041, 5081871122073, 230948185830187, 11449697796242319, 614944043618257237, 35568197580789653685, 2204201734650777596863, 145703352769994600516187, 10233323176300508748808921, 761004837938469796089586257
Offset: 0
-
a[0] = 1; a[n_] := a[n] = 3 n a[n - 1] + Sum[Binomial[n, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[1/(2 - 3 x - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
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;
Showing 1-4 of 4 results.