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A206735 Triangle T(n,k), read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 4
1, 0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 6, 4, 1, 0, 5, 10, 10, 5, 1, 0, 6, 15, 20, 15, 6, 1, 0, 7, 21, 35, 35, 21, 7, 1, 0, 8, 28, 56, 70, 56, 28, 8, 1, 0, 9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A103452*A007318 as infinite lower triangular matrices.

Essentially the same as A199011.

LINKS

Table of n, a(n) for n=0..77.

FORMULA

T(n,k) = A007318(n,k) - A073424(n,k).

Sum_{k, 0<=k<=n} T(n,k)*x^k = (1+x)^n - 1 + 0^n.

T(n,0) = 0^n = A000007(n), T(n,k) = binomial(n,k) for k>0.

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

Sum{k, 0<=k<=n} T(n,k)^x = A000027(n+1), A000225(n), A030662(n), A096191(n), A096192(n) for x = 0, 1, 2, 3, 4 respectively.

EXAMPLE

Triangle begins :

1

0, 1

0, 2, 1

0, 3, 3, 1

0, 4, 6, 4, 1

0, 5, 10, 10, 5, 1

0, 6, 15, 20, 15, 6, 1

0, 7, 21, 35, 35, 21, 7, 1

0, 8, 28, 56, 70, 56, 28, 8, 1

0, 9, 36, 84, 126, 126, 84, 36, 9, 1

0, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1

0, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1

CROSSREFS

Cf. A007318, A000071 (antidiagonal sums).

Sequence in context: A242378 A268820 A199011 * A089000 A253829 A107238

Adjacent sequences:  A206732 A206733 A206734 * A206736 A206737 A206738

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Feb 11 2012

STATUS

approved

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Last modified August 12 20:18 EDT 2022. Contains 356077 sequences. (Running on oeis4.)