OFFSET
0,5
COMMENTS
This triangle was inspired by a formula of Vladimir Kruchinin given in A001662.
EXAMPLE
[n\k 0, 1, 2, 3, 4, 5]
[0] 1,
[1] 0, 1,
[2] 0, 4, 3,
[3] 0, 24, 40, 15,
[4] 0, 192, 520, 420, 105,
[5] 0, 1920, 7392, 9520, 5040, 945,
MAPLE
MATHEMATICA
T[0, 0] = 1; T[n_, k_] := T[n, k] = Sum[Binomial[n+k, k-j]*(-1)^(n+k-j)* 2^(n-j)*Sum[Binomial[n+j, i]*StirlingS1[n+j-i, j-i], {i, 0, j}], {j, 0, k}];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] (* Jean-François Alcover, Jun 29 2019 *)
PROG
(Sage)
def A201636(n, k) :
if n==0 and k==0: return 1
return add(binomial(n+k, k-j)*(-1)^(k-j)*2^(n-j)*add(binomial(n+j, i)* stirling_number1(n+j-i, j-i) for i in (0..j)) for j in (0..k))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Nov 13 2012
STATUS
approved