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A220399 A convolution triangle of numbers obtained from A057682. 1
1, 0, 1, 0, 2, 1, 0, 3, 4, 1, 0, 3, 10, 6, 1, 0, 0, 18, 21, 8, 1, 0, -9, 21, 53, 36, 10, 1, 0, -27, 0, 99, 116, 55, 12, 1, 0, -54, -81, 117, 286, 215, 78, 14, 1, 0, -81, -270, -27, 528, 650, 358, 105, 16, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Triangle T(n,k) given by (0, 2, -1/2, 3/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

G.f.: (1-3*x+3*x^2)/(1-3*x-3*x*y+3*x^2+x^2*y)

G.f for k-th column: ((x-x^2)/(1-3*x+3*x^2))^k.

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - 3*T(n-2,k) - T(n-2,k-1), T(0,0) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k<0 or if k>n.

Sum_{k, 0<=k<=n, n>0} T(n,k) = A001792(n-1).

T(n+1,n) = 2*n = A005843(n).

T(n+2,n) = A014105(n).

T(n,1) = A057682(n).

EXAMPLE

Triangle begins :

1

0, 1

0, 2, 1

0, 3, 4, 1

0, 3, 10, 6, 1

0, 0, 18, 21, 8, 1

0, -9, 21, 53, 36, 10, 1

0, -27, 0, 99, 116, 55, 12, 1

CROSSREFS

Cf. A030523, A057682, A104597

Sequence in context: A049242 A108887 A193401 * A268830 A095884 A128908

Adjacent sequences:  A220396 A220397 A220398 * A220400 A220401 A220402

KEYWORD

sign,tabl

AUTHOR

Philippe Deléham, Feb 19 2013

STATUS

approved

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Last modified February 22 15:26 EST 2020. Contains 332137 sequences. (Running on oeis4.)