OFFSET
0,2
COMMENTS
The polynomial p(n,x) is defined by recursively by p(n,x)=(x+2n)*p(n-1,x) with p[0,x]=x. For an introduction to reductions of polynomials by substitutions such as x^2->x+2, see A192232.
Let transform T take the sequence {b(n), n>=1} to the sequence {c(n)} defined by: c(n) = det(M_n), where M_n denotes the n X n matrix with elements M_n(i,j) = b(2*j) for i>j and M_n(i,j) = b(i+j-1) for i<=j. Conjecture: a(n) = abs(c(n+1)), where c(n) denotes transform T of triangular numbers (A000217). - Lechoslaw Ratajczak, Jul 26 2021
FORMULA
a(n) = (1/3)*(2^(n+1)*(n+1)! + (2n-1)!!). - Vaclav Potocek, Feb 04 2016
EXAMPLE
MATHEMATICA
(See A192457.)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 01 2011
STATUS
approved