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A101854 a(n) = n*(n+1)*(n^2+21*n+50)/24. 3
6, 24, 61, 125, 225, 371, 574, 846, 1200, 1650, 2211, 2899, 3731, 4725, 5900, 7276, 8874, 10716, 12825, 15225, 17941, 20999, 24426, 28250, 32500, 37206, 42399, 48111, 54375, 61225, 68696, 76824, 85646, 95200, 105525, 116661, 128649, 141531, 155350 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

5th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 3: 1,4,1. 5th row of the array shown in A101853.

Partial sums of A101853.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

G.f.: x*(6-6*x+x^2)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

a(n) = 5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5), n>5. - Harvey P. Dale, Nov 05 2011

MATHEMATICA

Table[25 n/12+(71n^2)/24+(11n^3)/12+n^4/24, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {6, 24, 61, 125, 225}, 40] (* Harvey P. Dale, Nov 05 2011 *)

CROSSREFS

Sequence in context: A293017 A292889 A272951 * A273358 A325517 A101877

Adjacent sequences:  A101851 A101852 A101853 * A101855 A101856 A101857

KEYWORD

easy,nonn

AUTHOR

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004

EXTENSIONS

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.

Formula moved to be the definition by Eric M. Schmidt, Dec 12 2013

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)