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A246799 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x-3)^k. 1
1, 7, 2, 34, 20, 3, 142, 128, 39, 4, 547, 668, 309, 64, 5, 2005, 3098, 1929, 604, 95, 6, 7108, 13304, 10434, 4384, 1040, 132, 7, 24604, 54128, 51258, 27064, 8600, 1644, 175, 8, 83653, 211592, 234966, 149536, 59630, 15252, 2443, 224, 9, 280483, 802082, 1022286, 761896, 365810, 117312, 25123, 3464, 279, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Consider the transformation 1 + 2x + 3x^2 + 4x^3 + ... + (n+1)*x^n = A_0*(x-3)^0 + A_1*(x-3)^1 + A_2*(x-3)^2 + ... + A_n*(x-3)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
LINKS
FORMULA
T(n,0) = ((2*n+1)*3^(n+1) + 1)/4, for n >= 0.
T(n,n-1) = n*(3*n+4), for n >= 1.
Row n sums to A014916(n+1) = T(2*n+1,0) of A246788.
EXAMPLE
Triangle starts:
1;
7, 2;
34, 20, 3;
142, 128, 39, 4;
547, 668, 309, 64, 5;
2005, 3098, 1929, 604, 95, 6;
7108, 13304, 10434, 4384, 1040, 132, 7;
24604, 54128, 51258, 27064, 8600, 1644, 175, 8;
83653, 211592, 234966, 149536, 59630, 15252, 2443, 224, 9;
280483, 802082, 1022286, 761896, 365810, 117312, 25123, 3464, 279, 10;
...
PROG
(PARI) T(n, k) = (k+1)*sum(i=0, n-k, 3^i*binomial(i+k+1, k+1))
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")))
CROSSREFS
Sequence in context: A096900 A282799 A222555 * A248189 A096040 A038268
KEYWORD
nonn,tabl
AUTHOR
Derek Orr, Nov 15 2014
STATUS
approved

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Last modified April 21 00:22 EDT 2024. Contains 371850 sequences. (Running on oeis4.)