A206819 Riordan array (1/(1-10*x-10*x^2), x/(1-10*x-10*x^2)).

1, 10, 1, 90, 20, 1, 800, 280, 30, 1, 7100, 3400, 570, 40, 1, 63000, 38300, 8800, 960, 50, 1, 559000, 412000, 120600, 18000, 1450, 60, 1, 4960000, 4296000, 1530000, 291000, 32000, 2040, 70, 1

Offset

0,2

Comments

Row sums are A000042(n+1).

Subtriangle of triangle given by (0, 10, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Links

Table of n, a(n) for n=0..35.

Formula

T(n,k) = 10*T(n-1,k) - 10*T(n-2,k) + T(n-1,k-1).

G.f.: 1/(1-10*x+10*x^2-y*x).

Sum_{k, 0<=k} T(n,k)*x^k = A178869(n+1), A057086(n), A000042(n+1) for x = -1, 0, 1 respectively.

Example

Triangle begins :
1
10, 1
90, 20, 1
800, 280, 30, 1
7100, 3400, 570, 40, 1
63000, 38300, 8800, 960, 50, 1
559000, 412000, 120600, 18000, 1450, 60, 1
4960000, 4296000, 1530000, 291000, 32000, 2040, 70, 1
Triangle (0, 10, -1, 1, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) begins :
1
0, 1
0, 10, 1
0, 90, 20, 1
0, 800, 280, 30, 1
0, 7100, 3400, 570, 40, 1 ...

Crossrefs

Cf. A101950, A178865,

Sequence in context: A305996 A030526 A327003 * A178865 A347491 A164881

Adjacent sequences: A206816 A206817 A206818 * A206820 A206821 A206822

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Feb 12 2012

Status

approved