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A080851
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Square array of pyramidal numbers, read by antidiagonals.
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2
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1, 1, 3, 1, 4, 6, 1, 5, 10, 10, 1, 6, 14, 20, 15, 1, 7, 18, 30, 35, 21, 1, 8, 22, 40, 55, 56, 28, 1, 9, 26, 50, 75, 91, 84, 36, 1, 10, 30, 60, 95, 126, 140, 120, 45, 1, 11, 34, 70, 115, 161, 196, 204, 165, 55, 1, 12, 38, 80, 135, 196, 252, 288, 285, 220, 66, 1, 13, 42, 90, 155
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| T(n, k) = C(k+2, 2)+n*C(k+2, 3). T(n, k)=T(n-1, k)+C(k+2, 3) = T(n-1, k)+k(k+1)(k+2)/6 G.f. for rows : (1+nx)/(1-x)^4, n>=-1
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EXAMPLE
| Array (n>=0,k>=0) begins
1 3 6 10 15 21 28 ...
1 4 10 20 35 56 84 ...
1 5 14 30 55 91 140 ...
1 6 18 40 75 126 196 ...
1 7 22 50 95 161 252 ...
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PROG
| (Derive). vector(vector(poly_coeff(Taylor((1+kx)/(1-x)^4, x, 11), x, n), n, 0, 11), k, -1, 10) VECTOR(VECTOR(comb(k+2, 2)+comb(k+2, 3)n, k, 0, 11), n, 0, 11)
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CROSSREFS
| Numerous sequences in the database are to be found in the array. Rows include the pyramidal numbers A000217, A000292, A000330, A002411, A002412, A002413, A002414, A007584, A007585, A007586.
Columns include or are closely related to A017029, A017113, A017017, A017101, A016777, A017305. Diagonals include A006325, A006484, A002417.
Cf. A057145.
Sequence in context: A194540 A193043 A086271 * A108285 A075419 A060922
Adjacent sequences: A080848 A080849 A080850 * A080852 A080853 A080854
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 21 2003
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