A202328 Triangle T(n,k) = coefficient of x^n in expansion of [x(1+x^2)/(1-x^2)]^k = sum(n>=k, T(n,k) x^n).

1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 2, 0, 6, 0, 1, 0, 8, 0, 8, 0, 1, 2, 0, 18, 0, 10, 0, 1, 0, 12, 0, 32, 0, 12, 0, 1, 2, 0, 38, 0, 50, 0, 14, 0, 1, 0, 16, 0, 88, 0, 72, 0, 16, 0, 1, 2, 0, 66, 0, 170, 0, 98, 0, 18, 0, 1, 0, 20, 0, 192, 0, 292, 0, 128, 0, 20, 0, 1, 2, 0, 102, 0, 450, 0, 462, 0, 162, 0, 22, 0, 1, 0, 24, 0, 360, 0, 912, 0, 688, 0, 200, 0, 24, 0, 1

Offset

1,4

Links

Table of n, a(n) for n=1..105.

Formula

T(n,k)=((sum(i=0..(n-k)/2, binomial(k,(n-k)/2-i)*binomial(k+i-1,k-1)))*((-1)^(n+k)+1))/2.

Example

1
0, 1,
2, 0, 1,
0, 4, 0, 1,
2, 0, 6, 0, 1,
0, 8, 0, 8, 0, 1,
2, 0, 18, 0, 10, 0, 1

Prog

(Maxima)
T(n, k):=((sum(binomial(k, (n-k)/2-i)*binomial(k+i-1, k-1), i, 0, (n-k)/2))*((-1)^(n+k)+1))/2

Crossrefs

Sequence in context: A371093 A053389 A354667 * A136688 A131321 A111959

Adjacent sequences: A202325 A202326 A202327 * A202329 A202330 A202331

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Dec 17 2011

Status

approved