A025277 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.

0, 0, 1, 1, 0, 1, 2, 1, 2, 6, 6, 7, 20, 30, 34, 75, 140, 182, 322, 644, 972, 1554, 3024, 5091, 8052, 14784, 26378, 43032, 75504, 136994, 232232, 399399, 720356, 1257256, 2161874, 3852576, 6831552, 11858418, 20949304, 37350768

Offset

1,7

Links

Table of n, a(n) for n=1..40.

Formula

G.f.: -(sqrt(1-4*x^4-4*x^3)-1)/2. - Vladimir Kruchinin, Nov 21 2014

a(n) = sum(m=0..(n-3)/2, (binomial(n-2*m-3,m)*binomial(2*m+1,n-2*m-3))/(2*m+1)). - Vladimir Kruchinin, Nov 21 2014

a(n) = (4 - 24/n)*a(n-4) + (4 - 18/n)*a(n-3). - Robert Israel, Nov 21 2014

Maple

A025277:= gfun:-rectoproc({a(n) = (4 - 24/n)*a(n-4) + (4 - 18/n)*a(n-3), a(1)=0, a(2)=0, a(3)=1, a(4)=1}, a(n), remember):
seq(A025277(n), n=1..100); # Robert Israel, Nov 21 2014

Mathematica

nmax = 30; aa = ConstantArray[0, nmax]; aa[[1]] = 0; aa[[2]] = 0; aa[[3]] = 1; aa[[4]] = 1; Do[aa[[n]] = Sum[aa[[k]]*aa[[n-k]], {k, 1, n-1}], {n, 5, nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)
a[n_] := Sum[Binomial[n-2*m-3, m]*Binomial[2*m+1, n-2*m-3]/(2*m+1), {m, 0, (n-3)/2}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 03 2015, after Vladimir Kruchinin *)

Prog

(Maxima)
a(n):=sum((binomial(n-2*m-3, m)*binomial(2*m+1, n-2*m-3))/(2*m+1), m, 0, (n-3)/2); /* Vladimir Kruchinin, Nov 21 2014 */

Crossrefs

Sequence in context: A281781 A351317 A094965 * A248100 A153896 A074727

Adjacent sequences: A025274 A025275 A025276 * A025278 A025279 A025280

Keyword

nonn

Author

Clark Kimberling

Status

approved