A385526
E.g.f. A(x) satisfies A(x) = exp(x*A(3*x)).
Original entry on oeis.org
1, 1, 7, 208, 23365, 9588976, 14040296659, 71747056999360, 1255862559932597257, 74168744207577385109248, 14599375893944236344767578111, 9483024632344097320792984610415616, 20158786175666520486280070249843236771213, 139271933359690469686747131442731382830399594496
Offset: 0
-
nmax = 15; A[] = 1; Do[A[x] = E^(x*A[3*x]) + O[x]^j // Normal, {j, 1, nmax + 1}]; CoefficientList[A[x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 02 2025 *)
-
def ncr(n, r)
return 1 if r == 0
(n - r + 1..n).inject(:*) / (1..r).inject(:*)
end
def A(q, n)
ary = [1]
(1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + (j + 1) * q ** j * ncr(i - 1, j) * ary[j] * ary[i - 1 - j]}}
ary
end
def A385526(n)
A(3, n)
end
A385527
E.g.f. A(x) satisfies A(x) = exp(x*A(4*x)).
Original entry on oeis.org
1, 1, 9, 457, 118961, 152894961, 940318147705, 26967408304580857, 3534888068831469959649, 2084993641133372935803249505, 5465706581663919414225671125834601, 63043356313898446097762231466174924913065, 3173076775252515207774429654590479617164788572049
Offset: 0
-
nmax = 15; A[] = 1; Do[A[x] = E^(x*A[4*x]) + O[x]^j // Normal, {j, 1, nmax + 1}]; CoefficientList[A[x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 02 2025 *)
-
def ncr(n, r)
return 1 if r == 0
(n - r + 1..n).inject(:*) / (1..r).inject(:*)
end
def A(q, n)
ary = [1]
(1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + (j + 1) * q ** j * ncr(i - 1, j) * ary[j] * ary[i - 1 - j]}}
ary
end
def A385527(n)
A(4, n)
end
A385529
E.g.f. A(x) satisfies A(x) = exp(x*A(-3*x)).
Original entry on oeis.org
1, 1, -5, -152, 15949, 6548656, -9510189137, -48598095401792, 849885323784381337, 50192539805114962349824, -9878895951508580401879879229, -6416836884643090722807370469927936, 13640603845766595275775514993987722683941, 94239467260528503337471761892783659993298198528
Offset: 0
-
def ncr(n, r)
return 1 if r == 0
(n - r + 1..n).inject(:*) / (1..r).inject(:*)
end
def A(q, n)
ary = [1]
(1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + (j + 1) * q ** j * ncr(i - 1, j) * ary[j] * ary[i - 1 - j]}}
ary
end
def A385529(n)
A(-3, n)
end
A385530
E.g.f. A(x) satisfies A(x) = exp(x*A(-4*x)).
Original entry on oeis.org
1, 1, -7, -359, 90705, 116586321, -715618113143, -20523234900205911, 2689857437569063003169, 1586566688643256394542888225, -4159073515698730238218108546470759, -47972197129364591236078587520718376138951, 2414519164037893898620724924577882591112859773297
Offset: 0
-
def ncr(n, r)
return 1 if r == 0
(n - r + 1..n).inject(:*) / (1..r).inject(:*)
end
def A(q, n)
ary = [1]
(1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + (j + 1) * q ** j * ncr(i - 1, j) * ary[j] * ary[i - 1 - j]}}
ary
end
def A385530(n)
A(-4, n)
end
Showing 1-4 of 4 results.