A067534 a(n) = 4^n * sum_{i=1,n} i^4/4^i.

1, 20, 161, 900, 4225, 18196, 75185, 304836, 1225905, 4913620, 19669121, 78697220, 314817441, 1259308180, 5037283345, 20149198916, 80596879185, 322387621716, 1289550617185, 5158202628740, 20632810709441

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (9, -30, 50, -45, 21, -4).

Formula

1/81 * [380*4^n - 27n^4 - 144n^3 - 360n^2 - 528n - 380]. - Ralf Stephan, May 08 2004

a(1)=1, a(2)=20, a(3)=161, a(4)=900, a(5)=4225, a(6)=18196, a(n)= 9*a(n-1)- 30*a(n-2)+50*a(n-3)-45*a(n-4)+21*a(n-5)-4*a(n-6). - Harvey P. Dale, Jul 15 2012

From Peter Bala, Nov 29 2012, (Start)

Recurrence equation: a(n) = 4*a(n-1) + n^4. See A047520 and A066999.

O.g.f.: (x + 11*x^2 + 11*x^3 + x^4)/((1 - 4*x)*(1 - x)^5) = x + 20*x^2 + 161*x^3 + .... (end)

Mathematica

Table[4^n*Sum[i^4/4^i, {i, n}], {n, 30}] (* or *) LinearRecurrence[ {9, -30, 50, -45, 21, -4}, {1, 20, 161, 900, 4225, 18196}, 30] (* Harvey P. Dale, Jul 15 2012 *)

Crossrefs

Cf. A047520, A066999.

Sequence in context: A125357 A126515 A118676 * A041768 A221870 A289181

Adjacent sequences: A067531 A067532 A067533 * A067535 A067536 A067537

Keyword

nonn,easy

Author

Benoit Cloitre, Jan 27 2002

Status

approved