

A072405


Triangle of C(n,k)C(n2,k1).


10



1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 4, 7, 7, 4, 1, 1, 5, 11, 14, 11, 5, 1, 1, 6, 16, 25, 25, 16, 6, 1, 1, 7, 22, 41, 50, 41, 22, 7, 1, 1, 8, 29, 63, 91, 91, 63, 29, 8, 1, 1, 9, 37, 92, 154, 182, 154, 92, 37, 9, 1, 1, 10, 46, 129, 246, 336, 336, 246, 129, 46, 10, 1, 1, 11, 56
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OFFSET

0,8


COMMENTS

Starting 1,0,1,1,1,... this is the Riordan array ((1x+x^2)/(1x),x/(1x)). Its diagonal sums are A006355. Its inverse is A106509.  Paul Barry, May 04 2005


LINKS

Table of n, a(n) for n=0..80.


FORMULA

T(n, k)=T(n1, k1)+T(n1, k) starting with T(2, 0)=T(2, 1)=T(2, 2)=1.
G.f.: (1x^2y) / [1x(1+y)].  Ralf Stephan, Jan 31 2005


EXAMPLE

Rows start:
1;
1,1;
1,1,1; (key row for starting the recurrence)
1,2,2,1;
1,3,4,3,1;
1,4,7,7,4,1;
1,5,11,14,11,5,1;


MATHEMATICA

t[2, 1] = 1; t[n_, n_] = t[_, 0] = 1; t[n_, k_] := t[n, k] = t[n1, k1] + t[n1, k]; Table[t[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* JeanFrançois Alcover, Nov 28 2013, after Ralf Stephan *)


CROSSREFS

Row sums give essentially A003945, A007283, or A042950. Cf. A072406 for number of odd terms in each row.
Cf. A051597, A096646, A122218.
Sequence in context: A086461 A047089 A122218 * A146565 A115594 A086623
Adjacent sequences: A072402 A072403 A072404 * A072406 A072407 A072408


KEYWORD

easy,nonn,tabl


AUTHOR

Henry Bottomley, Jun 16 2002


STATUS

approved



