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A089663 Let S1 := (n,t)->add( k^t * add( binomial(n,j), j=0..k), k=0..n); a(n) = S1(n,6). 1
0, 2, 259, 6284, 77180, 646960, 4235864, 23313408, 112793088, 493969920, 1998346240, 7577934848, 27232132096, 93517705216, 308908943360, 986642513920, 3059995508736, 9247515082752, 27310549696512, 79012328898560, 224396746424320, 626707269681152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Jun Wang and Zhizheng Zhang, On extensions of Calkin's binomial identities, Discrete Math., 274 (2004), 331-342.

Index entries for linear recurrences with constant coefficients, signature (16,-112,448,-1120,1792,-1792,1024,-256)

FORMULA

There is an explicit formula for the sum - see Wang and Zhang.

From Chai Wah Wu, Jun 21 2016: (Start)

a(n) = 16*a(n-1) - 112*a(n-2) + 448*a(n-3) - 1120*a(n-4) + 1792*a(n-5) - 1792*a(n-6) + 1024*a(n-7) - 256*a(n-8) for n > 7.

G.f.: x*(-72*x^5 + 2096*x^4 + 4748*x^3 + 2364*x^2 + 227*x + 2)/(2*x - 1)^8. (End)

a(n) = 2^(n-7)*n*(381*n^6 + 1302*n^5 + 1302*n^4 + 420*n^3 - 707*n^2 - 378*n + 368)/21. - Ilya Gutkovskiy, Jun 21 2016

MATHEMATICA

LinearRecurrence[{16, -112, 448, -1120, 1792, -1792, 1024, -256}, {0, 2, 259, 6284, 77180, 646960, 4235864, 23313408}, 100] (* G. C. Greubel, Jun 22 2016 *)

CROSSREFS

Sequence in context: A128697 A182422 A218435 * A252708 A103029 A122862

Adjacent sequences:  A089660 A089661 A089662 * A089664 A089665 A089666

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 04 2004

STATUS

approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)