

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
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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(n1,k1) + 3*T(n1,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..(k1), n+j}/(3k(k1)!) (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^(n2), if (k==n, 1, if (k < n, T(n1, k1) + 3*T(n1, 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



