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A114188 Riordan array (1/(1-x),x(1+x)/(1-x)^2). 2
1, 1, 1, 1, 4, 1, 1, 9, 7, 1, 1, 16, 26, 10, 1, 1, 25, 70, 52, 13, 1, 1, 36, 155, 190, 87, 16, 1, 1, 49, 301, 553, 403, 131, 19, 1, 1, 64, 532, 1372, 1462, 736, 184, 22, 1, 1, 81, 876, 3024, 4446, 3206, 1216, 246, 25, 1, 1, 100, 1365, 6084, 11826, 11584, 6190, 1870, 317 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Product of A007318 and A113953, that is, (1/(1-x),x/(1-x))*(1,x(1+2x)).

Row sums are A025192. Diagonal sums are A052980.

Inverse is A114189. A signed version is A110511.

LINKS

Table of n, a(n) for n=0..63.

P. Barry, A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays, Journal of Integer Sequences, 16 (2013), #13.5.4.

FORMULA

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

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

T(n,k) = 2*T(n-1,k)+T(n-1,k-1)-T(n-2,k)+T(n-2,k-1), T(0,0)=T(1,0)=T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 11 2014

G.f.: 1/(1-y-x*(1+y)/(1-y)). - Vladimir Kruchinin, Apr 21 2015

EXAMPLE

Triangle begins

1;

1, 1;

1, 4, 1;

1, 9, 7, 1;

1, 16, 26, 10, 1;

1, 25, 70, 52, 13, 1;

1, 36,155,190, 87, 16, 1;

CROSSREFS

Cf. A007318, A025192, A052980, A110511, A113953, A114189.

Sequence in context: A183153 A208513 A141905 * A110511 A082950 A060102

Adjacent sequences:  A114185 A114186 A114187 * A114189 A114190 A114191

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Nov 16 2005

STATUS

approved

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Last modified June 21 04:47 EDT 2021. Contains 345355 sequences. (Running on oeis4.)