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A258310 T(n,k) = 1/k! * Sum_{i=0..k} (-1)^(k-i) *C(k,i) * A258309(n,i); triangle T(n,k), n>=0, 0<=k<=floor(n/2), read by rows. 4
1, 1, 2, 1, 4, 3, 9, 14, 3, 21, 50, 15, 51, 204, 122, 15, 127, 784, 644, 105, 323, 3212, 4115, 1310, 105, 835, 13068, 22587, 9270, 945, 2188, 55475, 137503, 85109, 16764, 945, 5798, 238073, 787127, 614779, 149754, 10395 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Rows n = 0..200, flattened

EXAMPLE

Triangle T(n,k) begins:

:    1;

:    1;

:    2,     1;

:    4,     3;

:    9,    14,      3;

:   21,    50,     15;

:   51,   204,    122,    15;

:  127,   784,    644,   105;

:  323,  3212,   4115,  1310,   105;

:  835, 13068,  22587,  9270,   945;

: 2188, 55475, 137503, 85109, 16764, 945;

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, (k*x+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..14);

CROSSREFS

Column k=0 gives A001006.

T(2n,n) gives A001147.

Row sums give A258311.

Cf. A258307, A258309.

Sequence in context: A262155 A181882 A109195 * A217927 A284709 A307365

Adjacent sequences:  A258307 A258308 A258309 * A258311 A258312 A258313

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, May 25 2015

STATUS

approved

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Last modified October 16 18:38 EDT 2019. Contains 328102 sequences. (Running on oeis4.)