The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A337169 a(n) = (-1)^n + 3 * Sum_{k=0..n-1} a(k) * a(n-k-1). 3
 1, 2, 13, 89, 691, 5720, 49555, 443630, 4071595, 38105342, 362271823, 3488988101, 33967656469, 333752559392, 3305347855573, 32960499084305, 330664662067795, 3335002912108670, 33796042027030855, 343940115478559699, 3513702627928096681, 36021007341027948032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Inverse binomial transform of A005159. LINKS FORMULA G.f. A(x) satisfies: A(x) = 1 / (1 + x) + 3*x*A(x)^2. G.f.: (1 - sqrt(1 - 12*x / (1 + x))) / (6*x). E.g.f.: exp(5*x) * (BesselI(0,6*x) - BesselI(1,6*x)). a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 3^k * Catalan(k). MATHEMATICA a[n_] := a[n] = (-1)^n + 3 Sum[a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}] Table[Sum[(-1)^(n - k) Binomial[n, k] 3^k CatalanNumber[k], {k, 0, n}], {n, 0, 21}] Table[(-1)^n Hypergeometric2F1[1/2, -n, 2, 12], {n, 0, 21}] CROSSREFS Cf. A000108, A005043, A005159, A337167, A337168. Sequence in context: A172968 A126035 A074617 * A199489 A300764 A209470 Adjacent sequences:  A337166 A337167 A337168 * A337170 A337171 A337172 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 28 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 16 03:46 EDT 2021. Contains 343937 sequences. (Running on oeis4.)