OFFSET
0,8
COMMENTS
Row sums are 1, 0, 1, 4, 1, -14, 1, 106, 1, -944, 1, 10396, 1, -135134, 1, 2027026, 1, -34459424, 1, 654729076, 1...
[Row sums s(n) appear to obey s(n) -2*s(n-1) +(n+1)*s(n-2) +2*(1-n)*s(n-3) +(n-2)* s(n-4)=0. - R. J. Mathar, Dec 04 2011]
REFERENCES
Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986, pp. 8, 42-43.
EXAMPLE
1;
1, -1;
1, -1, 1;
1, 2, 2, -1;
1, 6, -4, -3, 1;
1, -4, -20,6, 4, -1;
1, -40, 8, 44, -8, -5, 1;
1, -12, 188, -6, -80,10, 6, -1;
1, 308, 136, -546, -10, 130, -12, -7, 1;
1, 416, -1864, -628, 1256, 50, -196, 14, 8, -1;
1, -2664, -3640, 6696, 1984, -2506, -126,280, -16, -9, 1;
MAPLE
h := proc(n, x)
if n = 0 then
1 ;
elif n = 1 then
1-x ;
else
1+n-(1-x)*(1-procname(n-1, x)) -n*procname(n-2, x) ;
expand(%) ;
end if;
end proc:
A136247 := proc(n, k)
coeftayl(h(n, x), x=0, k) ;
end proc:
seq(seq(A136247(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Dec 04 2011
MATHEMATICA
Clear[h, a, n, x, y, c, d] (*Solve linear Shabat transform for Hermite type recursion*) Solve[c*x0 + d - x*(c*x1 + d) + n*(c*x2 + d) == 0, x0] c = -1; d = 1; Solve[y = c*x + d == 0, x] h[x, 0] = 1; h[x, 1] = 1 - x; h[x_, n_] := h[x, n] = -(-1 - n + (1 - x) - (1 - x)* h[ x, n - 1] + n *h[x, n - 2]); Table[ExpandAll[h[x, n]], {n, 0, 10}]; a = Table[CoefficientList[h[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[h[x, n], x]], {n, 0, 10}];
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 17 2008
STATUS
approved