OFFSET
0,5
COMMENTS
FORMULA
EXAMPLE
Triangle begins:
1;
1;
1, 1;
2, 3;
4, 9, 1;
10, 30, 6;
25, 100, 36, 1;
75, 370, 186, 10;
225, 1369, 961, 100, 1;
780, 5587, 4960, 750, 15;
2704, 22801, 25600, 5625, 225, 1;
10556, 101774, 136960, 39000, 2325, 21;
41209, 454276, 732736, 270400, 24025, 441, 1;
178031, 2199262, 4110512, 1849120, 217000, 6027, 28;
769129, 10647169, 23059204, 12645136, 1960000, 82369, 784, 1;
3630780, 55493841, 136074274, 87570056, 16787400, 944230, 13720, 36; ...
MATHEMATICA
S[n_, k_] = Sum[StirlingS2[n, i] Binomial[i, k], {i, 0, n}];
T[n_, k_] := S[Floor[n/2], k] S[Floor[(n+1)/2], k];
Table[T[n, k], {n, 0, 15}, {k, 0, Floor[n/2]}] // Flatten (* Jean-François Alcover, Nov 02 2020 *)
PROG
(PARI) {T(n, k) = (n\2)!*((n+1)\2)!*polcoeff(polcoeff(exp((1+y)*(exp(x+x*O(x^n))-1)), n\2), k) *polcoeff(polcoeff(exp((1+y)*(exp(x+x*O(x^n))-1)), (n+1)\2), k)}
for(n=0, 15, for(k=0, n\2, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paul D. Hanna, Nov 08 2006
STATUS
approved