OFFSET
0,2
COMMENTS
Mirror image of A013612. - Zerinvary Lajos, Nov 25 2007
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
Also the convolution triangle of A000351. - Peter Luschny, Oct 09 2022
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
B. N. Cyvin, J. Brunvoll, and S. J. Cyvin, Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), 109-121.
FORMULA
See A038207 and A027465 and replace 2 and 3 in analogous formulas with 5. - Tom Copeland, Oct 26 2012
EXAMPLE
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;
MAPLE
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.
PMatrix(10, n -> 5^(n-1)); # Peter Luschny, Oct 09 2022
MATHEMATICA
With[{q=5}, Table[q^(n-k)*Binomial[n, k], {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, May 12 2021 *)
PROG
(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
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved