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A081181 Staircase on Pascal's triangle. 4
1, 3, 6, 20, 35, 126, 210, 792, 1287, 5005, 8008, 31824, 50388, 203490, 319770, 1307504, 2042975, 8436285, 13123110, 54627300, 84672315, 354817320, 548354040, 2310789600, 3562467300, 15084504396, 23206929840, 98672427616, 151532656696 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Arrange Pascal's triangle as a square array. A081181 is then a diagonal staircase on the square array. A companion staircase is given by A065942.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

FORMULA

a(n) = binomial(floor((n + 1)/2) + (n + 1), n).

Conjecture: 8*n*(n+3)*(1845*n-2882)*a(n) +4*(-5097*n^3+11143*n^2+42110*n-27416)*a(n-1) +6*(-16605*n^3-7272*n^2-16701*n+9490)*a(n-2) +3*(3*n-5)*(5097*n-949)*(3*n-4)*a(n-3)=0. - R. J. Mathar, Oct 29 2014

MATHEMATICA

Table[Binomial[Floor[(n + 1) / 2] + (n + 1), n], {n, 0, 30}] (* Vincenzo Librandi, Aug 06 2013 *)

PROG

(MAGMA) [Binomial(Floor((n+1)/2)+(n+1), n): n in [0..30]]; // Vincenzo Librandi, Aug 06 2013

CROSSREFS

Sequence in context: A290784 A176993 A276748 * A062164 A265112 A052408

Adjacent sequences:  A081178 A081179 A081180 * A081182 A081183 A081184

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

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Last modified October 18 00:55 EDT 2019. Contains 328135 sequences. (Running on oeis4.)