A254147 a(n) = 1*9^n + 2*8^n + 3*7^n + 4*6^n + 5*5^n + 6*4^n + 7*3^n + 8*2^n + 9*1^n.

45, 165, 825, 4917, 32505, 229845, 1703625, 13072917, 103008345, 828707925, 6779099625, 56214660117, 471424600185, 3990804658005, 34053173154825, 292542431786517, 2527742384720025, 21950298188288085, 191434401453597225, 1675813243179972117

Offset

0,1

Comments

This is the sequence of ninth terms of "second partial sums of m-th powers".

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Luciano Ancora, Demonstration of formulas

Index entries for linear recurrences with constant coefficients, signature (45,-870,9450,-63273,269325,-723680,1172700,-1026576,362880).

Formula

G.f.: -3*(2333280*x^8 - 5080464*x^7 + 4500500*x^6 - 2143640*x^5 + 605675*x^4 - 104636*x^3 + 10850*x^2 - 620*x + 15) / ((x - 1)*(2*x - 1)*(3*x - 1)*(4*x - 1)*(5*x - 1)*(6*x - 1)*(7*x - 1)*(8*x - 1)*(9*x - 1)). - Colin Barker, Jan 28 2015

From Peter Bala, Jan 31 2016: (Start)

a(n) = (x + 1)*( Bernoulli(n + 1, x + 1) - Bernoulli(n + 1, 1) )/(n + 1) - ( Bernoulli(n + 2, x + 1) - Bernoulli(n + 2, 1) )/(n + 2) at x = 9.

a(n) = (1/8!)*Sum_{k = 0..n} (-1)^(k+n)*(k + 10)!*Stirling2(n,k) /((k + 1)*(k + 2)). (End)

Maple

seq(add(i*(10-i)^n, i = 1..9), n = 0..20); # Peter Bala, Jan 31 2017

Prog

(PARI) vector(30, n, n--; 8*2^n + 6*4^n + 2*8^n + 7*3^n + 4*6^n + 9^n + 5*5^n + 3*7^n + 9) \\ Colin Barker, Jan 28 2015

Crossrefs

Cf. A052548, A254028, A254030, A254031, A254144, A254145, A254146.

Sequence in context: A288669 A305069 A061658 * A271737 A280887 A158630

Adjacent sequences: A254144 A254145 A254146 * A254148 A254149 A254150

Keyword

nonn,easy

Author

Luciano Ancora, Jan 28 2015

Status

approved