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A254144 a(n) = 1*6^n + 2*5^n + 3*4^n + 4*3^n + 5*2^n + 6*1^n. 7
21, 56, 196, 812, 3724, 18236, 93436, 494732, 2685004, 14851676, 83384476, 473755052, 2717541484, 15709845116, 91395715516, 534498925772, 3139343105164, 18504595174556, 109397060622556, 648335998054892, 3850205790608044 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is the sequence of sixth 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 (21,-175,735,-1624,1764,-720).

FORMULA

G.f.: -(8028*x^5 - 13916*x^4 + 8939*x^3 - 2695*x^2 + 385*x - 21) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Jan 26 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 = 6.

a(n) = (1/5!)*Sum_{k = 0..n} (-1)^(k+n)*(k + 7)!*Stirling2(n,k)/ ((k + 1)*(k + 2)). (End)

MAPLE

seq(add(i*(7 - i)^n, i = 1..6), n = 0..20); # Peter Bala, Jan 31 2017

MATHEMATICA

Table[5 2^n + 3 4^n + 4 3^n + 2 5^n + 6^n + 6, {n, 0, 25}] (* Bruno Berselli, Jan 27 2015 *)

PROG

(PARI) Vec(-(8028*x^5-13916*x^4+8939*x^3-2695*x^2+385*x-21)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)) + O(x^100)) \\ Colin Barker, Jan 26 2015

CROSSREFS

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

Sequence in context: A145719 A031963 A067727 * A165237 A271734 A189004

Adjacent sequences:  A254141 A254142 A254143 * A254145 A254146 A254147

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Jan 26 2015

STATUS

approved

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Last modified February 27 18:28 EST 2020. Contains 332307 sequences. (Running on oeis4.)