This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A212280 G.f. A(x)=1/(1-F(x)), where F(F(x)) = (1 - sqrt(1-16*x))/8. 1
 1, 1, 3, 17, 131, 1177, 11531, 119201, 1276771, 14015401, 156585211, 1772626673, 20275611347, 233912585849, 2718842818923, 31816917837377, 374657837729987, 4436890509548617 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS F(x) is the generating function of A213422. LINKS Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation A^{2^n}(x)=F(x), arXiv:1302.1986 FORMULA a(n) = sum(m=1..n, T(n,m)) for n>0, where T(n,m)= 1 if n=m, otherwise = (m *4^(n-m) *binomial(2*n-m-1,n-1)/n - sum_{i=m+1..n-1} T(n,i)*T(i,m) )/2. MAPLE T := proc(n, m)     if n = m then         1 ;     else         m*4^(n-m)*binomial(2*n-m-1, n-1)/n ;         %-add(procname(n, i)*procname(i, m), i=m+1..n-1) ;         %/2 ;     end if; end proc: A212280 := proc(n)     if n = 0 then         1     else         add(T(n, m), m=1..n) ;     end if; end proc: # R. J. Mathar, Mar 04 2013 MATHEMATICA Clear[t]; t[n_, m_] := t[n, m] = 1/2*((m*4^(n-m)*Binomial[2*n-m-1, n-1]/n - Sum[ t[n, i]*t[i, m], {i, m+1, n-1}])); t[n_, n_] = 1; a[n_] := Sum[t[n, m], {m, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Feb 25 2013, from formula *) PROG (Maxima) Solve(k):=block([Tmp, i, j], array(Tmp, k, k), for i:0 thru k do for j:0 thru k do Tmp[i, j]:a, T(n, m):=if Tmp[n, m]=a then (if n=m then (Tmp[n, n]:1) else (Tmp[n, m]:(1/2*((m*4^(n-m)*binomial(2*n-m-1, n-1))/n-sum(T(n, i)*T(i, m), i, m+1, n-1))))) else Tmp[n, m],  makelist(sum(T(j, i), i, 1, j), j, 1, k)); CROSSREFS Cf. A213422. Sequence in context: A006759 A073513 A074524 * A307680 A305819 A163684 Adjacent sequences:  A212277 A212278 A212279 * A212281 A212282 A212283 KEYWORD nonn AUTHOR Vladimir Kruchinin, Feb 14 2013 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 June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)