A187920 Triangle T(n,k) for A(x)^k=sum(n>=k T(n,k)*x^n), where o.g.f. A(x) satisfies A(x)=(1+x*A(x)^3)/(1-x*A(x)^3).

1, 2, 1, 14, 4, 1, 134, 32, 6, 1, 1482, 324, 54, 8, 1, 17818, 3696, 578, 80, 10, 1, 226214, 45316, 6810, 904, 110, 12, 1, 2984206, 583152, 85278, 11008, 1310, 144, 14, 1, 40503890, 7769348, 1113854, 140936, 16490, 1804, 182, 16, 1, 561957362, 106250144, 15004746, 1870352, 216002, 23472, 2394, 224, 18, 1

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

T(n,k):=k/(3*n-2*k)*sum(i=0..n-k, binomial(3*n-2*k,n-k-i)*binomial(3*n-2*k+i-1,3*n-2*k-1)), n>=k>0.

Example

        1
        2         1
       14         4         1
      134        32         6         1
     1482       324        54         8         1
    17818      3696       578        80        10         1
   226214     45316      6810       904       110        12         1
  2984206    583152     85278     11008      1310       144        14         1
 40503890   7769348   1113854    140936     16490      1804       182        16         1
561957362 106250144  15004746   1870352    216002     23472      2394       224        18         1

Prog

(Maxima)
T(n, k):=k/(3*n-2*k)*sum(binomial(3*n-2*k, n-k-i)*binomial(3*n-2*k+i-1, 3*n-2*k-1), i, 0, n-k);

Crossrefs

Cf. A378238, A144097 (column k=1), A371675 (k=2), A365843 (k=3).

Sequence in context: A217475 A288298 A288762 * A338207 A063613 A245733

Adjacent sequences: A187917 A187918 A187919 * A187921 A187922 A187923

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Mar 16 2011

Status

approved