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A156141 Triangle T(n,k) = A008517(n,k+1)+A008517(n,n+1-k) read by rows. 3
2, 1, 1, 1, 4, 1, 1, 14, 14, 1, 1, 46, 116, 46, 1, 1, 172, 772, 772, 172, 1, 1, 834, 5160, 8800, 5160, 834, 1, 1, 5280, 39594, 90260, 90260, 39594, 5280, 1, 1, 40814, 361086, 981104, 1288040, 981104, 361086, 40814, 1, 1, 363884, 3801180, 12088796 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are 2*A001147(n).

LINKS

Table of n, a(n) for n=0..48.

E. W. Weisstein, Second-Order Eulerian Triangle

FORMULA

T(n,0)=T(n,n) =1, n>=1.

T(n,k)= A008517(n,k+1)+A008517(n,n+1-k), n>1, 0<k<n.

T(n,k)= T(n,n-k) .

EXAMPLE

{2},

{1, 1},

{1, 4, 1},

{1, 14, 14, 1},

{1, 46, 116, 46, 1},

{1, 172, 772, 772, 172, 1},

{1, 834, 5160, 8800, 5160, 834, 1},

{1, 5280, 39594, 90260, 90260, 39594, 5280, 1},

{1, 40814, 361086, 981104, 1288040, 981104, 361086, 40814, 1},

{1, 363884, 3801180, 12088796, 18205564, 18205564, 12088796, 3801180, 363884, 1},

{1, 3630826, 44557888, 167513072, 283669904, 310714768, 283669904, 167513072, 44557888, 3630826, 1}

MATHEMATICA

e[n_, 0] := 1;

e[n_, k_] := 0 /; k >= n;

e[n_, k_] := (k + 1)e[n - 1, k] + (2n - k - 1)e[n - 1, k - 1];

Table[Table[e[n, k] + e[n, n - k], {k, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Cf. A008517

Sequence in context: A260757 A157114 A156786 * A174555 A157113 A214712

Adjacent sequences:  A156138 A156139 A156140 * A156142 A156143 A156144

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Feb 04 2009

EXTENSIONS

Definition simplified by the Associate Editors of the OEIS Sep 17 2009

STATUS

approved

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Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)