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A058649 a(n) = 2^(n-4)*n*(n+1)*(n^2+5*n-2). 5
0, 1, 18, 132, 680, 2880, 10752, 36736, 117504, 357120, 1041920, 2939904, 8067072, 21618688, 56770560, 146472960, 372113408, 932511744, 2308571136, 5653135360, 13707509760, 32942063616, 78525759488, 185799278592, 436627046400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A000583.

REFERENCES

A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992.

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

FORMULA

a(n) = Sum_{i=1..n} i^4 * binomial(n, i).

G.f.: x*(8*x^2-8*x-1)/(2*x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009

a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5). - Wesley Ivan Hurt, Dec 24 2021

MATHEMATICA

LinearRecurrence[{10, -40, 80, -80, 32}, {0, 1, 18, 132, 680}, 30] (* Wesley Ivan Hurt, Dec 24 2021 *)

CROSSREFS

Cf. A000583.

Sequence in context: A299137 A299368 A299932 * A273222 A103308 A320677

Adjacent sequences:  A058646 A058647 A058648 * A058650 A058651 A058652

KEYWORD

nonn,easy

AUTHOR

Yong Kong (ykong(AT)curagen.com), Dec 26 2000

STATUS

approved

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Last modified June 30 12:41 EDT 2022. Contains 354939 sequences. (Running on oeis4.)