OFFSET
0,4
COMMENTS
FORMULA
EXAMPLE
Square array begins
n\k|.....0......1.......2.......3........4........5........6
============================================================
..0|.....1......1.......1.......1........1........1........1
..1|.....1......3.......5.......7........9.......11.......13
..2|.....3.....11......27......51.......83......123......171
..3|....11.....57.....175.....413......819.....1441.....2327
..4|....57....361....1353....3801.....8857....18057....33321
..5|...361...2763...12125...39487...105489...244211...507013
..6|..2763..24611..123987..458331..1379003..3569523..8229891
..
Examples of recurrence relation:
T(4,3) = 3801 = 3*T(3,2) + 4*T(3,4) = 3*175 + 4*819;
T(5,1) = 2763 = 1*T(4,0)+ 2*T(4,2) = 1*57 + 2*1353.
MAPLE
# A185418
S := proc(n, x) option remember; description `polynomials S(n, x)`;
if n = 0 then 1 else x*S(n-1, x-1)+(x+1)*S(n-1, x+1) end if end proc:
for n from 0 to 10 do seq(S(n, k), k = 0..10) end do;
MATHEMATICA
T[n_, k_] := T[n, k] = If[n<0 || k<0, 0, If[n == 0, 1, k T[n-1, k-1] + (k+1)*T[n-1, k+1]]];
Table[T[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 22 2021 *)
PROG
(PARI) {T(n, k)=if(n<0|k<0, 0, if(n==0, 1, k*T(n-1, k-1)+(k+1)*T(n-1, k+1)))}
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Jan 30 2011
STATUS
approved