This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A289066 Recurrence a(n+2) = Sum_{k=0..n} binomial(n,k)*a(k)*a(n+1-k) with a(0)=3, a(1)=1. 15
 3, 1, 3, 10, 39, 184, 1047, 7000, 53571, 460936, 4404603, 46296040, 530878719, 6595091944, 88232942847, 1264741738120, 19337532032091, 314144393039176, 5403576523773603, 98110258621524520, 1875097757416854999, 37629001852534817704, 791088129700026499047 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS One of a family of integer sequences whose e.g.f.s satisfy the differential equation f''(z) = f'(z)f(z). For more details, see A289064. LINKS Stanislav Sykora, Table of n, a(n) for n = 0..200 S. Sykora, Sequences related to the differential equation f'' = af'f, Stan's Library, Vol. VI, Jun 2017. FORMULA E.g.f.: -sqrt(7)/tanh(z*sqrt(7)/2 - arccosh(3/sqrt(2))). E.g.f. for the sequence (-1)^(n+1)*a(n): -sqrt(7)/tanh(z*sqrt(7)/2 + arccosh(3/sqrt(2))). a(n) ~ 2 * n! * 7^((n+1)/2) / log(8 + 3*sqrt(7))^(n+1). - Vaclav Kotesovec, Jun 24 2017 MAPLE f:= proc(n) option remember; add(binomial(n-2, k)*procname(k)*procname(n-1-k), k=0..n-2) end proc: f(0):= 3: f(1):= 1: map(f, [\$0..50]); # Robert Israel, Jul 20 2017 MATHEMATICA a[n_] := a[n] = Sum[Binomial[n-2, k]*a[k]*a[n-k-1], {k, 0, n-2}]; a[0] = 3; a[1] = 1; Array[a, 23, 0] (* Jean-François Alcover, Jul 20 2017 *) PROG (PARI) c0=3; c1=1; nmax = 200; a = vector(nmax+1); a[1]=c0; a[2]=c1; for(m=0, #a-3, a[m+3]=sum(k=0, m, binomial(m, k)*a[k+1]*a[m+2-k])); a CROSSREFS Sequences for other starting pairs: A000111 (1,1), A289064 (1,-1), A289065 (2,-1), A289067 (3,-1), A289068 (1,-2), A289069 (3,-2), A289070 (0,3). Sequence in context: A170860 A170845 A025238 * A126970 A204134 A233168 Adjacent sequences:  A289063 A289064 A289065 * A289067 A289068 A289069 KEYWORD nonn AUTHOR Stanislav Sykora, Jun 23 2017 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 December 19 03:45 EST 2018. Contains 318245 sequences. (Running on oeis4.)