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A258307
T(n,k) = 1/k! * Sum_{i=0..k} (-1)^(k-i) *C(k,i) * A258306(n,i); triangle T(n,k), n>=0, 0<=k<=floor(n/2), read by rows.
5
1, 1, 2, 1, 5, 2, 14, 9, 1, 43, 28, 3, 141, 114, 21, 1, 490, 421, 82, 4, 1785, 1750, 442, 38, 1, 6789, 7114, 1941, 180, 5, 26809, 30854, 9868, 1210, 60, 1, 109632, 134239, 46337, 6191, 335, 6, 462755, 609276, 235035, 37321, 2700, 87, 1, 2012441, 2800134, 1157603, 199424, 15806, 560, 7
OFFSET
0,3
LINKS
EXAMPLE
Triangle T(n,k) begins:
: 1;
: 1;
: 2, 1;
: 5, 2;
: 14, 9, 1;
: 43, 28, 3;
: 141, 114, 21, 1;
: 490, 421, 82, 4;
: 1785, 1750, 442, 38, 1;
: 6789, 7114, 1941, 180, 5;
: 26809, 30854, 9868, 1210, 60, 1;
MAPLE
b:= proc(x, y, t, k) option remember; `if`(y>x or y<0, 0,
`if`(x=0, 1, b(x-1, y-1, false, k)*`if`(t, (x+k*y)/y, 1)
+b(x-1, y, false, k) +b(x-1, y+1, true, k)))
end:
A:= (n, k)-> b(n, 0, false, k):
T:= proc(n, k) option remember;
add(A(n, i)*(-1)^(k-i)*binomial(k, i), i=0..k)/k!
end:
seq(seq(T(n, k), k=0..n/2), n=0..13);
MATHEMATICA
b[x_, y_, t_, k_] := b[x, y, t, k] = If[y > x || y < 0, 0, If[x == 0, 1, b[x - 1, y - 1, False, k]*If[t, (x + k*y)/y, 1] + b[x - 1, y, False, k] + b[x - 1, y + 1, True, k]]];
A[n_, k_] := b[n, 0, False, k];
T[n_, k_] := T[n, k] = Sum[A[n, i]*(-1)^(k-i)*Binomial[k, i], {i, 0, k}]/ k!;
Table[T[n, k], {n, 0, 13}, {k, 0, n/2}] // Flatten (* Jean-François Alcover, Jun 06 2018, from Maple *)
CROSSREFS
Column k=0 gives A258312.
Row sums give A258308.
Sequence in context: A364487 A192263 A109738 * A343254 A143891 A030400
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, May 25 2015
STATUS
approved