A211399 Triangle T(n,k), 0 <= k <= n, given by (0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...) DELTA (1, 0, 3, 0, 5, 0, 7, 0, 9, 0, ...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 1, 0, 1, 5, 1, 0, 1, 15, 18, 1, 0, 1, 37, 129, 58, 1, 0, 1, 83, 646, 877, 179, 1, 0, 1, 177, 2685, 8030, 5280, 543, 1, 0, 1, 367, 10002, 56285, 82610, 29658, 1636, 1, 0, 1, 749, 34777, 335162

Offset

0,9

Comments

Contains A156920 as submatrix.

Row-reversal of A102365. - Philippe Deléham, Feb 12 2013

Links

Table of n, a(n) for n=0..49.

Formula

T(n,k) = k*T(n-1,k) + (2n-2k+1)*T(n-1,k-1) , T(n,n) = 1, T(n,k) = 0 if k<0 or if k>n.

T(n,k) = A185411(n,k)/(2^(n-k)).

Sum_{k, 0<=k<=n} T(n,k)*x^(n-k) = A000012(n), A014307(n), A001147(n) for x = 0, 1, 2 respectively .

G.f.: 1/(1-xy/(1-x/(1-3xy/(1-2x/(1-5xy/(1-3x/(1-7xy/(1- ...(continued fraction).

Example

Triangle begins :
1
0, 1
0, 1, 1
0, 1, 5, 1
0, 1, 15, 18, 1
0, 1, 37, 129, 58, 1
0, 1, 83, 646, 877, 179, 1

Crossrefs

Left hand column sequences: A000007, A000012, A050488, A142965, A142966, A142968.

Right hand column sequences: A000340, A156922, A156923, A156924.

Row sums A014307(n).

Sequence in context: A007912 A019755 A085475 * A265192 A157012 A102365

Adjacent sequences: A211396 A211397 A211398 * A211400 A211401 A211402

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Feb 08 2013

Status

approved