A171243 Riordan array (f(x), x*g(x)), f(x) is the g.f. of A126952, g(x) is the g.f. of A117641.

1, 1, 1, 5, 1, 1, 21, 6, 1, 1, 93, 25, 7, 1, 1, 421, 112, 29, 8, 1, 1, 1937, 510, 132, 33, 9, 1, 1, 9017, 2357, 606, 153, 37, 10, 1, 1, 42349, 11009, 2819, 709, 175, 41, 11, 1, 1, 200277, 51840, 13233, 3324, 819, 198, 45, 12, 1, 1

Offset

0,4

Comments

Expansion of row sums of T_(x,3), T_(x,y) defined in A039599.

Matrix product P^3 * Q * P^(-3), where P denotes Pascal's triangle A007318 and Q denotes A061554 (formed from P by sorting the rows into descending order). Cf. A158793 and A158815. - Peter Bala, Jul 13 2021

Links

Table of n, a(n) for n=0..54.

Formula

Sum_{k=0..n} T(n,k)*x^k = A126952(n), A126568(n), A026375(n), A026378(n+1), A000351(n) for x = 0,1,2,3,4 respectively.

Example

Triangle begins:
    1;
    1,   1;
    5,   1,  1;
   21,   6,  1, 1;
   93,  25,  7, 1, 1;
  421, 112, 29, 8, 1, 1;
  ...

Crossrefs

Cf. A061554, A158793, A158815, A171224.

Sequence in context: A262307 A144397 A047909 * A111577 A176242 A036969

Adjacent sequences: A171240 A171241 A171242 * A171244 A171245 A171246

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 06 2009

Status

approved