A186333 Triangle T(n,k), the coefficient of x^n in x^k*(1+x+x^2+2*x^3)^k, 1<=k<=n.

1, 1, 1, 1, 2, 1, 2, 3, 3, 1, 0, 6, 6, 4, 1, 0, 5, 13, 10, 5, 1, 0, 4, 18, 24, 15, 6, 1, 0, 4, 21, 43, 40, 21, 7, 1, 0, 0, 25, 64, 85, 62, 28, 8, 1, 0, 0, 18, 90, 151, 150, 91, 36, 9, 1, 0, 0, 12, 100, 245, 306, 245, 128, 45, 10, 1, 0, 0, 8, 97, 340, 561, 560, 378, 174, 55, 11, 1

Offset

1,5

Comments

The Riordan array (1,x+x^2+x^3+2*x^4) without the column k=0.

Links

Table of n, a(n) for n=1..78.

Vladimir Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

Formula

T(n,k) = sum_{j=0..k} binomial(k,j) *sum_{i=0..n-k} binomial(j,i) *binomial(k-j,n-3*k+2*j-i) *2^(n-3*k+2*j-i), n>0, n>=k.

Example

1,
1,1,
1,2,1,
2,3,3,1,
0,6,6,4,1,
0,5,13,10,5,1,
0,4,18,24,15,6,1,
0,4,21,43,40,21,7,1,
0,0,25,64,85,62,28,8,1,
0,0,18,90,151,150,91,36,9,1,
0,0,12,100,245,306,245,128,45,10,1,
0,0,8,97,340,561,560,378,174,55,11,1

Crossrefs

Sequence in context: A077876 A095056 A337557 * A272917 A239627 A101933

Adjacent sequences: A186330 A186331 A186332 * A186334 A186335 A186336

Keyword

nonn,tabl,easy

Author

Vladimir Kruchinin, Feb 17 2011

Status

approved