A080419 - OEIS

A080419

Triangle of generalized Chebyshev coefficients.

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

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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