This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A101478 G.f. satisfies A(x) = x*(1+A)^4/(1+A^2). 2
 0, 1, 4, 21, 124, 782, 5144, 34845, 241196, 1697498, 12104872, 87246770, 634425752, 4647805372, 34267130928, 254035385949, 1892315106252, 14155536314786, 106288436980488, 800753707211430, 6050872882024520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS M. Bousquet-Mélou, Limit laws for embedded trees FORMULA G.f. (1-(1-8*x)^(1/4))/(1+(1-8*x)^(1/4))-1, a(n)=sum(m=1..n, m*sum(k=0..n-m(-1)^(n-m-k)*binomial(n+k-1,n-1)*sum(j=0..k, binomial(j,n-m-3*k+2*j)*binomial(k,j)*2^(2*n-2*m-5*k+3*j)*3^(-n+m+3*k-j))))/n, n>0, a(0)=0. - Vladimir Kruchinin, Dec 10 2011 a(n) ~ 2^(3*n-1)/(Gamma(3/4)*n^(5/4)) * (1 - 2*Gamma(3/4)/ (n^(1/4)*sqrt(Pi)) + 3*Gamma(3/4)^2/(sqrt(2*n)*Pi)). - Vaclav Kotesovec, Sep 16 2013 Conjecture: n*(n-1)*(n+1)*a(n) -12*n*(n-1)*(2*n-3)*a(n-1) +12*(n-1)*(16*n^2-64*n+65)*a(n-2) -16*(2*n-5)*(4*n-9)*(4*n-11)*a(n-3)=0. - R. J. Mathar, Nov 10 2013 MAPLE A:= proc(n) option remember; if n=0 then 0 else convert(series(x* (1+A(n-1))^4/ (1+A(n-1)^2), x, n+1), polynom) fi end: a:= n-> coeff(A(n), x, n): seq(a(n), n=0..20); # Alois P. Heinz, Aug 23 2008 MATHEMATICA a[0]=0; a[n_] := Sum[m*Sum[(-1)^(n-m-k)*Binomial[n+k-1, n-1]*Sum[Binomial[j, n-m-3*k+2*j]*Binomial[k, j]*2^(2*n-2*m-5*k+3*j)*3^(-n+m+3*k-j), {j, 0, k}], {k, 0, n-m}], {m, 1, n}]/n; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 30 2015, after Vladimir Kruchinin *) PROG (Maxima) a(n):=sum(m*sum((-1)^(n-m-k)*binomial(n+k-1, n-1)*sum(binomial(j, n-m-3*k+2*j)*binomial(k, j)*2^(2*n-2*m-5*k+3*j)*3^(-n+m+3*k-j), j, 0, k), k, 0, n-m), m, 1, n)/n; (* Vladimir Kruchinin, Dec 10 2011 *) CROSSREFS Sequence in context: A003014 A108404 A115136 * A153291 A244062 A093965 Adjacent sequences:  A101475 A101476 A101477 * A101479 A101480 A101481 KEYWORD nonn AUTHOR Ralf Stephan, Jan 21 2005 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 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)