OFFSET
0,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1274
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
2, 5, 5, 2;
3, 11, 16, 11, 3;
6, 26, 50, 50, 26, 6;
11, 60, 143, 188, 143, 60, 11;
23, 142, 404, 656, 656, 404, 142, 23;
...
MATHEMATICA
B[m_] := Module[{u}, u = Table[0, {m}]; u[[1]] = 1; For[n = 1, n <= Length[u] - 1, n++, u[[n + 1]] = (1 + y)*(Sum[u[[i]]*u[[n + 1 - i]], {i, 1, n}] + If[OddQ[n], u[[Quotient[n, 2] + 1]] /. y -> y^2, 0])/2]; u];
CoefficientList[#, y]& /@ B[11] // Flatten (* Jean-François Alcover, Sep 24 2019, from PARI *)
PROG
(PARI)
B(n)={my(u=vector(n)); u[1]=1; for(n=1, #u-1, u[n+1]=(1+y)*(sum(i=1, n, u[i]*u[n+1-i]) + if(n%2, subst(u[n\2+1], y, y^2)))/2); u}
{ my(A=B(10)); for(n=1, #A, print(Vec(A[n]))) } \\ Andrew Howroyd, May 21 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Serena, May 17 2014
EXTENSIONS
Edited by Nathaniel Johnston, Sep 11 2014
Missing term inserted and a(45) and beyond from Andrew Howroyd, May 21 2018
STATUS
approved