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A072405 Triangle of C(n,k)-C(n-2,k-1). 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Starting 1,0,1,1,1,... this is the Riordan array ((1-x+x^2)/(1-x),x/(1-x)). 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(n-1, k-1)+T(n-1, k) starting with T(2, 0)=T(2, 1)=T(2, 2)=1.

G.f.: (1-x^2y) / [1-x(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[n-1, k-1] + t[n-1, k]; Table[t[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-Fran├žois 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

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Last modified December 10 13:38 EST 2016. Contains 279004 sequences.