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A110506 Riordan array (1/(1-xc(2x)),xc(2x)/(1-xc(2x))), c(x) the g.f. of A000108. 6
1, 1, 1, 3, 4, 1, 13, 19, 7, 1, 67, 102, 44, 10, 1, 381, 593, 278, 78, 13, 1, 2307, 3640, 1795, 568, 121, 16, 1, 14589, 23231, 11849, 4051, 999, 173, 19, 1, 95235, 152650, 79750, 28770, 7820, 1598, 234, 22, 1, 636925, 1025965, 545680, 204760, 59650, 13642, 2392, 304, 25, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Deleham triangle Delta(0^n,2-0^n) [see construction in A084938]. The binomial transform of the inverse of this triangle has general element (-2)^(n-k)*C(k,n-k), that is, it is the Riordan array (1,x(1-2x)) [A110509]. Row sums are A052701. Diagonal sums are A110508. Inverse is A110511.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

T(0,0) = 1, T(n,k) = Sum_{j=0..n} j*C(2n-j-1,n-j) * C(j,k) * 2^(n-j))/n.

T(n,k) = (-1)^(n-k)*A114189(n,k). - Philippe Deléham, Mar 24 2007

EXAMPLE

Rows begin:

1;

1,1;

3,4,1;

13,19,7,1;

67,102,44,10,1;

381,593,278,78,13,1;

From Philippe Deléham, Dec 01 2015: (Start)

Production matrix begins:

1, 1

2, 3, 1

2, 4, 3, 1

2, 4, 4, 3, 1

2, 4, 4, 4, 3, 1

2, 4, 4, 4, 4, 3, 1

2, 4, 4, 4, 4, 4, 3, 1

(End)

MATHEMATICA

{{1}}~Join~Table[Sum[j Binomial[2 n - j - 1, n - j] Binomial[j, k] 2^(n - j), {j, 0, n}]/n, {n, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, Dec 01 2015 *)

PROG

(PARI) tabl(nn)= {for (n=0, nn, for (k=0, n, if (n==0, x = 0^k, x = sum(j=0, n, j*binomial(2*n-j-1, n-j)*binomial(j, k)*2^(n-j)/n)); print1(x, ", "); ); print(); ); } \\ Michel Marcus, Jun 18 2015

CROSSREFS

Cf. A000108, A052701, A084938, A110508, A110509, A110511, A114189.

Sequence in context: A123319 A076785 * A114189 A200659 A059110 A100326

Adjacent sequences:  A110503 A110504 A110505 * A110507 A110508 A110509

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jul 24 2005

STATUS

approved

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Last modified February 24 13:14 EST 2018. Contains 299623 sequences. (Running on oeis4.)