A026950 a(n) = Sum_{k=0..n} (k+1) * T(n,k), with T given by A026374.

1, 3, 10, 25, 75, 175, 500, 1125, 3125, 6875, 18750, 40625, 109375, 234375, 625000, 1328125, 3515625, 7421875, 19531250, 41015625, 107421875, 224609375, 585937500, 1220703125, 3173828125, 6591796875, 17089843750, 35400390625, 91552734375, 189208984375, 488281250000

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,10,0,-25).

Crossrefs

Cf. A026374.

Programs

PARI

a(n) = (n + 2) * (7 + 3*(-1)^n) * 5^((n-1)\2) / 4 \\ Andrew Howroyd, Dec 27 2024

Formula

a(n) = (n + 2) * (7 + 3*(-1)^n) * 5^floor((n-1)/2) / 4.

From Colin Barker, Oct 13 2012: (Start)

a(n) = 10*a(n-2) - 25*a(n-4).

G.f.: -(5*x^3-3*x-1)/(5*x^2-1)^2. (End)

Extensions

a(28) onwards from Andrew Howroyd, Dec 27 2024