OFFSET
0,2
FORMULA
Let E(x) = Sum_{n>=0} x^n/((2n)!/2^n). Then Sum_{n>=0} Sum{k=0..n} T(n,k) y^k*x^n/((2n)!/2^n) = E(y*x) * E(x)^2.
EXAMPLE
1,
2, 1,
8, 12, 1,
32, 120, 30, 1,
128, 896, 560, 56, 1,
512, 5760, 6720, 1680, 90, 1
MATHEMATICA
nn = 8; ev[x_] := Sum[x^n/((2 n)!/2^n), {n, 0, nn}];
Map[Select[#, # > 0 &] &, Table[(2 n)!/2^n, {n, 0, nn}] CoefficientList[Series[ev[x]^2 ev[y x], {x, 0, nn}], {x, y}]] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jun 07 2020
STATUS
approved