A058649 a(n) = 2^(n-4)*n*(n+1)*(n^2+5*n-2).

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

Offset: 0

Author

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

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A000583.

Programs

Mathematica

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

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