A351437
G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^2.
Original entry on oeis.org
1, 1, 1, 3, 7, 17, 47, 145, 481, 1691, 6295, 24805, 103095, 449805, 2052081, 9762699, 48334855, 248568321, 1325297879, 7312927481, 41694974649, 245288605059, 1487041552343, 9279329735685, 59537092965663, 392371097100373, 2653606218921673, 18400405626141667, 130712743774279015
Offset: 0
-
nmax = 28; A[] = 0; Do[A[x] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k + 1] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]
A351283
G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^4.
Original entry on oeis.org
1, 1, 1, 5, 16, 46, 142, 496, 1888, 7538, 31291, 135739, 617461, 2939215, 14575027, 75014471, 399901294, 2205630124, 12572140372, 73961880118, 448447331338, 2798640572516, 17956583819425, 118336081817953, 800278211629795, 5549154792085813, 39420390891260821
Offset: 0
-
nmax = 26; A[] = 0; Do[A[x] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n + 1, k + 3] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]
A351648
G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - x)) / (1 - x)^5.
Original entry on oeis.org
1, 1, 1, 6, 22, 69, 224, 819, 3296, 13942, 60941, 276399, 1309207, 6479609, 33377271, 178186018, 983386188, 5604262733, 32955823822, 199771724691, 1246747659198, 8000380516898, 52728354046939, 356593588048023, 2472544614851517, 17563971319301049, 127727505109579581
Offset: 0
-
nmax = 26; A[] = 0; Do[A[x] = 1 + x + x^2 A[x/(1 - x)]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n + 2, k + 4] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]
Showing 1-3 of 3 results.