A355111
Expansion of e.g.f. 3 / (4 - 3*x - exp(3*x)).
Original entry on oeis.org
1, 2, 11, 93, 1041, 14541, 243747, 4767183, 106556373, 2679469065, 74864397015, 2300883358995, 77144051804409, 2802027511061325, 109604157405491691, 4593512301562215783, 205348466229473678301, 9753645833118762303249, 490530576727430107027839, 26040317900991310393061499
Offset: 0
-
nmax = 19; CoefficientList[Series[3/(4 - 3 x - Exp[3 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 3^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
A367836
Expansion of e.g.f. 1/(2 - x - exp(3*x)).
Original entry on oeis.org
1, 4, 41, 627, 12759, 324543, 9906453, 352785933, 14358074211, 657405969075, 33444798498657, 1871613674744553, 114259520317835871, 7556674046930376111, 538212358684663414317, 41071433946325564954581, 3343141735414440335583003
Offset: 0
-
With[{nn=20},CoefficientList[Series[1/(2-x-Exp[3x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 16 2024 *)
-
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;
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]!
A343674
a(0) = 1; a(n) = 4 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
Original entry on oeis.org
1, 5, 51, 781, 15947, 407021, 12466251, 445452813, 18191122219, 835737327661, 42661645147403, 2395510523568845, 146739531459316587, 9737742346694258157, 695911661109898805323, 53286006304099668950413, 4352120920347139791200171, 377674509364714706139413933, 34702277449656625185428239755
Offset: 0
-
a[0] = 1; a[n_] := a[n] = 4 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 (1 - 2 x) - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
Showing 1-4 of 4 results.