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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 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.)