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A171243 Riordan array (f(x), x*g(x)), f(x) is the g.f. of A126952, g(x) is the g.f. of A117641. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)