A027467 - OEIS

A027467

Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).

1, 15, 1, 225, 30, 1, 3375, 675, 45, 1, 50625, 13500, 1350, 60, 1, 759375, 253125, 33750, 2250, 75, 1, 11390625, 4556250, 759375, 67500, 3375, 90, 1, 170859375, 79734375, 15946875, 1771875, 118125, 4725, 105, 1, 2562890625, 1366875000, 318937500, 42525000, 3543750, 189000, 6300, 120, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

Numerators of lower triangle of (a[i,j])^4 where a[i,j] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.

Sum_{k=0..n} T(n,k)*x^k = (15 + x)^n.

EXAMPLE

Triangle begins:

15, 1;

225, 30, 1;

3375, 675, 45, 1;

50625, 13500, 1350, 60, 1;

759375, 253125, 33750, 2250, 75, 1;

11390625, 4556250, 759375, 67500, 3375, 90, 1;

170859375, 79734375, 15946875, 1771875, 118125, 4725, 105, 1;

2562890625, 1366875000, 318937500, 42525000, 3543750, 189000, 6300, 120, 1;

MATHEMATICA

Table[Binomial[n, k]15^(n-k), {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Dec 31 2017 *)

PROG

(Magma) [(15)^(n-k)*Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, May 12 2021

(Sage) flatten([[(15)^(n-k)*binomial(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 12 2021

CROSSREFS

Sequences of the form q^(n-k)*binomial(n, k): A007318 (q=1), A038207 (q=2), A027465 (q=3), A038231 (q=4), A038243 (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), this sequence (q=15).

Sequence in context: A131514 A049327 A030527 * A049375 A049224 A223517

Adjacent sequences: A027464 A027465 A027466 * A027468 A027469 A027470

KEYWORD

nonn,tabl

AUTHOR

Olivier Gérard

EXTENSIONS

Simpler definition from Philippe Deléham, Nov 10 2008

STATUS

approved