

A114188


Riordan array (1/(1x),x(1+x)/(1x)^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
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OFFSET

0,5


COMMENTS

Product of A007318 and A113953, that is, (1/(1x),x/(1x))*(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, jk)2^(jk).
T(n, k) = Sum_{j=0..nk} C(k, j)*C(n+kj, 2k).
T(n,k) = 2*T(n1,k)+T(n1,k1)T(n2,k)+T(n2,k1), 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/(1yx*(1+y)/(1y)).  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



