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A155755 Triangle t(n,m)= A143491(n+2,m+2)+A143491(n+2,n-m+2) read by rows. 0
2, 3, 3, 7, 10, 7, 25, 35, 35, 25, 121, 168, 142, 168, 121, 721, 1064, 735, 735, 1064, 721, 5041, 8055, 5399, 3330, 5399, 8055, 5041, 40321, 69299, 49371, 22449, 22449, 49371, 69299, 40321, 362881, 663740, 509830, 223300, 109298, 223300, 509830, 663740 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are (n+2)!.

This symmetric summation of the triangle A143491 is equivalent to the coefficient [x^m] (p_n(x)+x^n*p_n(1/x)) of the polynomials defined in A143491 plus their reverses.

LINKS

Table of n, a(n) for n=0..43.

EXAMPLE

2;

3, 3;,

7, 10, 7;

25, 35, 35, 25;

121, 168, 142, 168, 121;

721, 1064, 735, 735, 1064, 721;

5041, 8055, 5399, 3330, 5399, 8055, 5041;

40321, 69299, 49371, 22449, 22449, 49371, 69299, 40321;

362881, 663740, 509830, 223300, 109298, 223300, 509830, 663740, 362881;

3628801, 6999894, 5755002, 2672648, 902055, 902055, 2672648, 5755002, 6999894, 3628801;

MATHEMATICA

Clear[p, a, b, c, d, n, q, q2, x];

q[x_, n_] = Product[x + n - i + 1, {i, 0, n - 1}];

p[x_, n_] = q[x, n] + x^n*q[1/x, n];

Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];

a = Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A117524 A045683 A157531 * A080088 A098715 A167886

Adjacent sequences:  A155752 A155753 A155754 * A155756 A155757 A155758

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Jan 26 2009

STATUS

approved

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Last modified January 22 18:41 EST 2019. Contains 319365 sequences. (Running on oeis4.)