A013612 Triangle of coefficients in expansion of (1+5x)^n.

1, 1, 5, 1, 10, 25, 1, 15, 75, 125, 1, 20, 150, 500, 625, 1, 25, 250, 1250, 3125, 3125, 1, 30, 375, 2500, 9375, 18750, 15625, 1, 35, 525, 4375, 21875, 65625, 109375, 78125, 1, 40, 700, 7000, 43750, 175000, 437500, 625000, 390625, 1, 45, 900, 10500, 78750, 393750, 1312500, 2812500, 3515625, 1953125

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

Comments

Mirror image of A038243. - Zerinvary Lajos, Nov 25 2007

T(n,k) equals the number of n-length words on {0,1,...,5} having n-k zeros. - Milan Janjic, Jul 24 2015

Links

• Alois P. Heinz, Rows n = 0..140, flattened

Programs

Maple

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+5*x)^n):
seq(T(n), n=0..10);  # Alois P. Heinz, Jun 10 2014

Mathematica

row[n_] := CoefficientList[(1 + 5x)^n, x]; Table[row[n], {n, 0, 9}] // Flatten (* Jean-François Alcover, Feb 13 2016 *)

Formula

G.f.: 1 / [1 - x(1+5y)].

T(n,k) = 5^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k) *C(n,i) *4^(n-i). Row sums are 6^n = A000400(n). - Mircea Merca, Apr 28 2012