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A038243
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Triangle whose (i,j)-th entry is 5^(i-j)*binomial(i,j).
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7
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1, 5, 1, 25, 10, 1, 125, 75, 15, 1, 625, 500, 150, 20, 1, 3125, 3125, 1250, 250, 25, 1, 15625, 18750, 9375, 2500, 375, 30, 1, 78125, 109375, 65625, 21875, 4375, 525, 35, 1, 390625, 625000, 437500, 175000, 43750, 7000, 700, 40, 1, 1953125, 3515625, 2812500, 1312500, 393750, 78750, 10500, 900, 45, 1
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OFFSET
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0,2
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COMMENTS
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T(i,j) is the number of i-permutations of 6 objects a,b,c,d,e,f, with repetition allowed, containing j a's. - Zerinvary Lajos, Dec 21 2007
Triangle of coefficients in expansion of (5+x)^n - N-E. Fahssi, Apr 13 2008
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins as:
1;
5, 1;
25, 10, 1;
125, 75, 15, 1;
625, 500, 150, 20, 1;
3125, 3125, 1250, 250, 25, 1;
15625, 18750, 9375, 2500, 375, 30, 1;
78125, 109375, 65625, 21875, 4375, 525, 35, 1;
390625, 625000, 437500, 175000, 43750, 7000, 700, 40, 1;
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MAPLE
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for i from 0 to 8 do seq(binomial(i, j)*5^(i-j), j = 0 .. i) od; # Zerinvary Lajos, Dec 21 2007
# Uses function PMatrix from A357368. Adds column 1, 0, 0, ... to the left.
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MATHEMATICA
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With[{q=5}, Table[q^(n-k)*Binomial[n, k], {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, May 12 2021 *)
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PROG
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(Magma) [5^(n-k)*Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, May 12 2021
(Sage) flatten([[5^(n-k)*binomial(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 12 2021
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CROSSREFS
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Sequences of the form q^(n-k)*binomial(n, k): A007318 (q=1), A038207 (q=2), A027465 (q=3), A038231 (q=4), this sequence (q=5), A038255 (q=6), A027466 (q=7), A038279 (q=8), A038291 (q=9), A038303 (q=10), A038315 (q=11), A038327 (q=12), A133371 (q=13), A147716 (q=14), A027467 (q=15).
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KEYWORD
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AUTHOR
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STATUS
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approved
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