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A101164 Triangle read by rows: Delannoy numbers minus binomial coefficients. 8
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 7, 3, 0, 0, 4, 15, 15, 4, 0, 0, 5, 26, 43, 26, 5, 0, 0, 6, 40, 94, 94, 40, 6, 0, 0, 7, 57, 175, 251, 175, 57, 7, 0, 0, 8, 77, 293, 555, 555, 293, 77, 8, 0, 0, 9, 100, 455, 1079, 1431, 1079, 455, 100, 9, 0, 0, 10, 126, 668, 1911, 3191, 3191, 1911 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

T(n,2) = A005449(n-2) for n>1;

T(n,3) = A101165(n-3) for n>2;

T(n,4) = A101166(n-4) for n>3;

sum of n-th row = A094706(n).

LINKS

Reinhard Zumkeller, Rows n = 0..100 of table, flattened

Eric Weisstein's World of Mathematics, Delannoy Number

Eric Weisstein's World of Mathematics, Binomial Coefficient

Index entries for triangles and arrays related to Pascal's triangle

FORMULA

T(n, k) = TD(n, k) - Binomial(n, k), 0<=k<=n, where Binomial=A007318 and TD defines the triangle of A008288.

PROG

(Haskell)

a101164 n k = a101164_tabl !! n !! k

a101164_row n = a101164_tabl !! n

a101164_tabl = zipWith (zipWith (-)) a008288_tabl a007318_tabl

-- Reinhard Zumkeller, Jul 30 2013

CROSSREFS

Cf. A225413.

Sequence in context: A265080 A228275 A228250 * A229079 A254040 A062275

Adjacent sequences:  A101161 A101162 A101163 * A101165 A101166 A101167

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Dec 03 2004

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)