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A080419 Triangle of generalized Chebyshev coefficients. 5
1, 4, 1, 15, 7, 1, 54, 36, 10, 1, 189, 162, 66, 13, 1, 648, 675, 360, 105, 16, 1, 2187, 2673, 1755, 675, 153, 19, 1, 7290, 10206, 7938, 3780, 1134, 210, 22, 1, 24057, 37908, 34020, 19278, 7182, 1764, 276, 25, 1, 78732, 137781, 139968, 91854, 40824, 12474, 2592 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Second binomial transform of 'pruned' Pascal triangle Binomial(i+1,j+1), (i,j>=0).

LINKS

Table of n, a(n) for n=1..52.

FORMULA

T(n,1) = A006234(n+2), T(n,n) = 1, T(n,k) = T(n-1,k-1) + 3*T(n-1,k), T(n,k)=0 for k>n. - corrected by Michel Marcus, Apr 15 2018

As a square array, T1(n, k)= (n+3k)3^n Product{j=1..(k-1), n+j}/(3k(k-1)!) (k>=1, n>=0).

EXAMPLE

Rows are:

{1},

{4,1},

{15,7,1},

{54,36,10,1},

{189,162,66,13,1},

...

For example, 10 = 7+3*1, 66 = 36+3*10.

PROG

(PARI) T(n, k) = if (k==1, (n+2)*3^(n-2), if (k==n, 1, if (k < n, T(n-1, k-1) + 3*T(n-1, k), 0)));

tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Apr 15 2018

CROSSREFS

Columns include A006234, A080420, A080421, A080422, A080423.

Sequence in context: A319039 A107873 A156290 * A095307 A159764 A124029

Adjacent sequences:  A080416 A080417 A080418 * A080420 A080421 A080422

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Feb 19 2003

STATUS

approved

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Last modified December 14 07:03 EST 2019. Contains 329978 sequences. (Running on oeis4.)