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A121574 Riordan array (1/(1-2*x), x*(1+x)/(1-2*x)). 2
1, 2, 1, 4, 5, 1, 8, 16, 8, 1, 16, 44, 37, 11, 1, 32, 112, 134, 67, 14, 1, 64, 272, 424, 305, 106, 17, 1, 128, 640, 1232, 1168, 584, 154, 20, 1, 256, 1472, 3376, 3992, 2641, 998, 211, 23, 1, 512, 3328, 8864, 12592, 10442, 5221, 1574, 277, 26, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are A006190(n+1); diagonal sums are A077939.

Inverse is A121575.

A generalized Delannoy number triangle.

Antidiagonal sums are A002478. - Philippe Deléham, Nov 10 2011.

LINKS

G. C. Greubel, Rows n=0..100 of triangle, flattened

FORMULA

Number array T(n,k)=sum{j=0..n-k, C(k,j)C(n-j,k)2^(n-k-j)}

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k-1). - From Philippe Deléham, Nov 10 2011

EXAMPLE

Triangle begins

1

2, 1

4, 5, 1

8, 16, 8, 1

16, 44, 37, 11, 1

32, 112, 134, 67, 14, 1

64, 272, 424, 305, 106, 17, 1

MAPLE

T:=(n, k)->add(binomial(k, j)*binomial(n-j, k)*2^(n-k-j), j=0..n-k): seq(seq(T(n, k), k=0..n), n=0..9); # Muniru A Asiru, Nov 02 2018

MATHEMATICA

Table[Sum[Binomial[k, j] Binomial[n-j, k] 2^(n-k-j), {j, 0, n-k}], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 02 2018 *)

PROG

(PARI) for(n=0, 10, for(k=0, n, print1(sum(j=0, n-k, binomial(k, j)* binomial(n-j, k)*2^(n-k-j)), ", "))) \\ G. C. Greubel, Nov 02 2018

(MAGMA) [[(&+[ Binomial(k, j)*Binomial(n-j, k)*2^(n-k-j): j in [0..(n-k)]]): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Nov 02 2018

(GAP) T:=Flat(List([0..9], n->List([0..n], k->Sum([0..n-k], j->Binomial(k, j)*Binomial(n-j, k)*2^(n-k-j))))); # Muniru A Asiru, Nov 02 2018

CROSSREFS

Cf. Diagonals : A000012, A016789, A080855, A000079, A053220.

Sequence in context: A248670 A080935 A102661 * A117317 A124237 A123876

Adjacent sequences:  A121571 A121572 A121573 * A121575 A121576 A121577

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Aug 08 2006

STATUS

approved

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Last modified September 20 16:48 EDT 2019. Contains 327242 sequences. (Running on oeis4.)