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A086873 Triangle read by rows in which row n >= 1 gives coefficients in expansion of the polynomial Sum_{k=1..n} (1/n)*binomial(n,k)*binomial(n,k-1)*x^(2k)*(1+x)^(2n-2k) / x^2 in powers of x. 1
1, 1, 2, 2, 1, 4, 9, 10, 5, 1, 6, 21, 44, 57, 42, 14, 1, 8, 38, 116, 240, 336, 308, 168, 42, 1, 10, 60, 240, 680, 1392, 2060, 2160, 1530, 660, 132, 1, 12, 87, 430, 1545, 4152, 8449, 13014, 14985, 12540, 7227, 2574, 429, 1, 14, 119, 700, 3045, 10122, 26173, 53048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row n has 2n-1 terms.

LINKS

Table of n, a(n) for n=1..57.

C. Coker, Enumerating a class of lattice paths, Discrete Math., 271 (2003), 13-28.

EXAMPLE

For n=3 the polynomial is 1 + 4x + 9x^2 + 10x^3 + 5x^4.

  1;

  1,  2,  2;

  1,  4,  9,  10,    5;

  1,  6, 21,  44,   57,   42,   14;

  1,  8, 38, 116,  240,  336,  308,   168,    42;

  1, 10, 60, 240,  680, 1392, 2060,  2160,  1530,   660,  132;

  1, 12, 87, 430, 1545, 4152, 8449, 13014, 14985, 12540, 7227, 2574, 429;

MAPLE

j := 0:f := n->sum(binomial(n, k)*binomial(n, k-1)/n*x^(2*k)*(1+x)^(2*n-2*k), k=1..n): for n from 1 to 15 do p := expand(f(n)/x^2):for l from 0 to 2*n-2 do j := j+1: a[j] := coeff(p, x, l):od:od:seq(a[l], l=1..j); # Sascha Kurz

PROG

(PARI) for(n=1, 8, p=sum(k=1, n, (1/n)*binomial(n, k)*binomial(n, k-1)*x^(2*k)*(1+x)^(2*n-2*k))/x^2; for(i=1, 2*n-1, print1(polcoeff(p, i-1) ", "); ); print; ); \\ Ray Chandler, Sep 17 2003

CROSSREFS

A059231 gives row sums.

Sequence in context: A295687 A087854 A185041 * A101560 A291260 A218529

Adjacent sequences:  A086870 A086871 A086872 * A086874 A086875 A086876

KEYWORD

nonn,easy,tabf

AUTHOR

N. J. A. Sloane, Sep 16 2003

EXTENSIONS

More terms from Vladeta Jovovic and Ray Chandler, Sep 17 2003

STATUS

approved

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Last modified November 17 05:59 EST 2018. Contains 317275 sequences. (Running on oeis4.)