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A101097 a(n) =  n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840. 16
1, 12, 69, 272, 846, 2232, 5214, 11088, 21879, 40612, 71643, 121056, 197132, 310896, 476748, 713184, 1043613, 1497276, 2110273, 2926704, 3999930, 5393960, 7184970, 9462960, 12333555, 15919956, 20365047, 25833664, 32515032, 40625376, 50410712 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Fourth partial sums of cubes (A000578). Partial sums of A101094.

LINKS

Table of n, a(n) for n=1..31.

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube. [broken link]

FORMULA

This sequence could be obtained from the general formula a(n) = n*(n+1)*(n+2)*(n+3)* ... *(n+k)*(n*(n+k) + (k-1)*k/6)/((k+3)!/6) at k=4. - Alexander R. Povolotsky, May 17 2008

G.f.: x*(1+4*x+x^2)/(1-x)^8. - R. J. Mathar, Jun 13 2008

a(n) = Sum_{k=1,..,n} A000217(k)^2*A000217(n-k+1). - Bruno Berselli, Sep 04 2013

MATHEMATICA

Table[n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(2 + 4*n + n^2)/840, {n, 0, 50}] (* G. C. Greubel, Feb 17 2017 *)

PROG

(PARI) {A101097(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840} \\ R. J. Mathar, Dec 06 2011

(MAGMA) A000217:=func<i | i*(i+1)/2>; [&+[A000217(k)^2*A000217(n-k+1): k in [1..n]]: n in [1..40]]; // Bruno Berselli, Sep 04 2013

CROSSREFS

Cf. A000217, A101102, A101094, A024166, A000537.

Sequence in context: A096425 A212753 A210427 * A067702 A163193 A088832

Adjacent sequences:  A101094 A101095 A101096 * A101098 A101099 A101100

KEYWORD

nonn,easy

AUTHOR

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004

EXTENSIONS

Edited by Ralf Stephan, Dec 16 2004

STATUS

approved

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Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)