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A275327 Triangle read by rows, Riordan array (1, (2+(x-1)/(2*x^2)*(1-sqrt(1-4*x^2)))/ sqrt(1-4*x^2)). 2
1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 2, 7, 3, 1, 0, 10, 10, 12, 4, 1, 0, 5, 33, 25, 18, 5, 1, 0, 35, 42, 78, 48, 25, 6, 1, 0, 14, 144, 144, 155, 80, 33, 7, 1, 0, 126, 168, 420, 356, 275, 122, 42, 8, 1, 0, 42, 610, 723, 1018, 736, 450, 175, 52, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

Table starts:

[n] [k=0,1,2,...] row sum

[0] [1] 1

[1] [0, 1] 1

[2] [0, 1, 1] 2

[3] [0, 3, 2, 1] 6

[4] [0, 2, 7, 3, 1] 13

[5] [0, 10, 10, 12, 4, 1] 37

[6] [0, 5, 33, 25, 18, 5, 1] 87

[7] [0, 35, 42, 78, 48, 25, 6, 1] 235

[8] [0, 14, 144, 144, 155, 80, 33, 7, 1] 578

[9] [0, 126, 168, 420, 356, 275, 122, 42, 8, 1] 1518

MAPLE

S := proc(n, k) option remember; local ecn:

if n = 0 then return n^k fi;

ecn := n -> n!/(iquo(n, 2)!^2)/(iquo(n, 2)+1);

add(ecn(i)*S(n-1, k-i), i=1..k-n+1) end:

A275327 := (n, k) -> S(k, n):

seq(seq(A275327(n, k), k=0..n), n=0..8);

MATHEMATICA

(* The function RiordanArray is defined in A256893. *)

RiordanArray[1&, (2+(#-1)/(2#^2) (1-Sqrt[1-4#^2]))/Sqrt[1-4#^2]&, 11] // Flatten (* Jean-Fran├žois Alcover, Jul 16 2019 *)

PROG

(Sage) # Function riordan_array defined in A256893.

s = (2+(x-1)/(2*x^2)*(1-sqrt(1-4*x^2)))/sqrt(1-4*x^2)

riordan_array(1, s, 12)

CROSSREFS

Cf. A057977 (column 1), A128899, A275328.

Sequence in context: A250486 A316826 A256449 * A215486 A083721 A158459

Adjacent sequences:  A275324 A275325 A275326 * A275328 A275329 A275330

KEYWORD

nonn,tabl,changed

AUTHOR

Peter Luschny, Aug 16 2016

STATUS

approved

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Last modified July 22 17:02 EDT 2019. Contains 325225 sequences. (Running on oeis4.)