A351757
G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 3*x)) / (1 - 3*x)^2.
Original entry on oeis.org
1, 1, 7, 43, 289, 2239, 19699, 192025, 2042971, 23520715, 291099349, 3849621019, 54110928355, 804827487493, 12619011606775, 207885167529523, 3587864566792753, 64705561315720135, 1216574535057705979, 23797327657083197113, 483390249416359706995
Offset: 0
-
nmax = 20; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 3 x)]/(1 - 3 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 3^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
A351810
G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 4*x)) / (1 - 4*x)^2.
Original entry on oeis.org
1, 1, 9, 69, 565, 5305, 56929, 680685, 8902349, 126121313, 1923133433, 31379181461, 544931376229, 10024917092105, 194602995875985, 3972686705253181, 85035210652191485, 1903471938128641457, 44453001710603619369, 1080789854059236415973, 27304602412815047204501
Offset: 0
-
nmax = 20; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 4 x)]/(1 - 4 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
A351811
G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 5*x)) / (1 - 5*x)^2.
Original entry on oeis.org
1, 1, 11, 101, 971, 10621, 133251, 1872261, 28840251, 481539021, 8658919571, 166768522101, 3421884596011, 74443313899901, 1710104876681571, 41338914172638021, 1048412294411955451, 27821558652073329261, 770663280948805164051, 22235353608667471453621
Offset: 0
-
nmax = 19; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 5 x)]/(1 - 5 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 5^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
A351812
G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 6*x)) / (1 - 6*x)^2.
Original entry on oeis.org
1, 1, 13, 139, 1531, 19021, 271453, 4358179, 76896931, 1471496341, 30333401893, 670125430219, 15784342627531, 394467249489661, 10415430504486733, 289527454704656659, 8447556960083354131, 258008113711846390981, 8228947382557338981973, 273472796359924298018299
Offset: 0
-
nmax = 19; A[] = 0; Do[A[x] = 1 + x A[x/(1 - 6 x)]/(1 - 6 x)^2 + O[x]^(nmax + 1) // Normal,nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 6^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
A352859
a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k+1) * 2^k * a(k).
Original entry on oeis.org
1, 1, 4, 25, 280, 5665, 211516, 14907673, 2021820016, 535262714881, 279317901141172, 289064917007756761, 595455410823115765768, 2446703815513439818406305, 20077597428602000393057306476, 329252263598282049972950683567705, 10794203801863458962317873561872563680
Offset: 0
-
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k + 1] 2^k a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; A[] = 0; Do[A[x] = 1 + x A[2 x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Showing 1-5 of 5 results.