A354553
Expansion of e.g.f. exp( x * exp(x^3) ).
Original entry on oeis.org
1, 1, 1, 1, 25, 121, 361, 3361, 42001, 275185, 1819441, 30777121, 371238121, 3057311401, 44263763545, 801096528961, 9710981323681, 125367419194081, 2643123767954401, 45840730383002305, 646414025466298681, 13258301279836276441
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3)))))
-
a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(k!*(n-3*k)!));
A367720
E.g.f. satisfies A(x) = exp(x*A(x^4)).
Original entry on oeis.org
1, 1, 1, 1, 1, 121, 721, 2521, 6721, 196561, 3659041, 29993041, 159762241, 1686639241, 60298558321, 987112886761, 9315623640961, 76611297104161, 2454331471018561, 69805324167893281, 1086439146068753281, 62621251106366355481, 1358219171406244427281
Offset: 0
-
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)\4, (4*j+1)*v[j+1]*v[i-4*j]/(j!*(i-1-4*j)!))); v;
A356630
a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(n - 4*k)!.
Original entry on oeis.org
1, 1, 1, 1, 1, 121, 721, 2521, 6721, 378001, 7287841, 59930641, 319429441, 7524471241, 353072319601, 5897248517161, 55827317669761, 726274560953761, 53139878190826561, 1650487849152976801, 25981849479032542081, 317292238756098973081
Offset: 0
-
a[n_] := n! * Sum[(n - 4*k)^k/(n - 4*k)!, {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)
-
a(n) = n!*sum(k=0, n\4, (n-4*k)^k/(n-4*k)!);
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^4)))))
Showing 1-3 of 3 results.
Comments