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A263689 a(n) = (2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12. 1
1, 1, 2, 34, 277, 1301, 4426, 12202, 29009, 61777, 120826, 220826, 381877, 630709, 1002002, 1539826, 2299201, 3347777, 4767634, 6657202, 9133301, 12333301, 16417402, 21571034, 28007377, 35970001, 45735626, 57617002, 71965909, 89176277, 109687426, 133987426, 162616577, 196171009, 235306402, 280741826 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

G.f.: (1 - 6*x + 16*x^2 + 6*x^3 + 81*x^4 + 20*x^5 + 2*x^6)/(1 - x)^7.

a(n + 1) = a(n) + n^5, a(0) = 1.

a(n + 1) - a(n) = A000584(n).

a(n + 1) = A000539(n) + 1.

Sum_{n>0} 1/(a(n + 1) - a(n)) = zeta(5) = 1.036927755...

EXAMPLE

a(0) = 1,

a(1) = 0^5 + 1 = 1,

a(2) = 1^5 + 1 = 2,

a(3) = 2^5 + 2 = 34,

a(4) = 3^5 + 34 = 227,

a(5) = 4^5 + 227 = 1301, etc.

MATHEMATICA

Table[(1/12) (12 + (-1 + n)^2 n^2 (-1 + 2 (-1 + n) n)), {n, 0, 35}]

PROG

(PARI) first(m)=vector(m, n, n--; (2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12) \\ Anders Hellström, Nov 20 2015

CROSSREFS

Cf. A000124, A000539, A000584, A056520, A154323.

Sequence in context: A036827 A136362 A220507 * A098531 A296995 A301611

Adjacent sequences:  A263686 A263687 A263688 * A263690 A263691 A263692

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Nov 20 2015

STATUS

approved

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Last modified November 18 07:22 EST 2019. Contains 329252 sequences. (Running on oeis4.)