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A118931 Triangle, read by rows, where T(n,k) = n!/[k!*(n-3*k)!*3^k)] for n>=3*k>=0. 3
1, 1, 1, 1, 2, 1, 8, 1, 20, 1, 40, 40, 1, 70, 280, 1, 112, 1120, 1, 168, 3360, 2240, 1, 240, 8400, 22400, 1, 330, 18480, 123200, 1, 440, 36960, 492800, 246400, 1, 572, 68640, 1601600, 3203200, 1, 728, 120120, 4484480, 22422400, 1, 910, 200200, 11211200 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row n contains 1+floor(n/3) terms. Row sums yield A001470. Given column vector V = A118932, then V is invariant under matrix product T*V = V, or, A118932(n) = Sum_{k=0..n} T(n,k)*A118932(k). Given C = Pascal's triangle and T = this triangle, then matrix product M = C^-1*T yields M(3n,n) = (3*n)!/(n!*3^n), 0 otherwise (cf. A100861 formula due to Paul Barry).

LINKS

Table of n, a(n) for n=0..48.

FORMULA

E.g.f.: A(x,y) = exp(x + y*x^3/3).

EXAMPLE

Triangle T begins:

1;

1;

1;

1,2;

1,8;

1,20;

1,40,40;

1,70,280;

1,112,1120;

1,168,3360,2240;

1,240,8400,22400;

1,330,18480,123200;

1,440,36960,492800,246400; ...

PROG

(PARI) T(n, k)=if(n<3*k, 0, n!/(k!*(n-3*k)!*3^k))

CROSSREFS

Cf. A001470 (row sums), A118932 (invariant vector); variants: A100861, A118933.

Sequence in context: A008308 A176889 A208753 * A101280 A008309 A131175

Adjacent sequences:  A118928 A118929 A118930 * A118932 A118933 A118934

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, May 06 2006

STATUS

approved

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Last modified December 3 04:39 EST 2016. Contains 278698 sequences.