Search: id:A060354
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%I A060354
%S A060354 0,1,2,6,16,35,66,112,176,261,370,506,672,871,1106,1380,1696,2057,
%T A060354 2466,2926,3440,4011,4642,5336,6096,6925,7826,8802,9856,10991,12210,
%U A060354 13516,14912,16401,17986,19670,21456,23347,25346,27456,29680,32021
%N A060354 The n-th n-gonal number.
%C A060354 Binomial transform of (0,1,0,3,0,0,0,....). - Paul Barry (pbarry(AT)wit.ie), 
               Sep 14 2006
%H A060354 Harry J. Smith, <a href="b060354.txt">Table of n, a(n) for n=0,...,1000</
               a>
%F A060354 a(n) = (n(n-2)^2+n^2)/2
%F A060354 E.g.f.: exp(x)*x*(1+x^2/2); - Paul Barry (pbarry(AT)wit.ie), Sep 14 2006
%F A060354 sum((binomial(0,0*j)+binomial(n,2)),j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Sep 04 2006
%F A060354 G.f.: x(1-2x+4x^2)/(1-x)^4. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 02 2008]
%F A060354 G.f.: exp(x)*(x+x^3/2) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 05 2009]
%p A060354 restart: G(x):=exp(x)*(x+x^3/2): f[0]:=G(x): for n from 1 to 45 do f[n]:=diff(f[n-1],
               x) od: x:=0: seq(f[n],n=0..41);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 05 2009]
%o A060354 (PARI) { for (n=0, 1000, write("b060354.txt", n, " ", (n*(n - 2)^2 + 
               n^2)/2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 
               04 2009]
%Y A060354 First differences of A004255.
%Y A060354 Sequence in context: A071522 A005996 A032091 this_sequence A140131 A159938 
               A145126
%Y A060354 Adjacent sequences: A060351 A060352 A060353 this_sequence A060355 A060356 
               A060357
%K A060354 easy,nice,nonn
%O A060354 0,3
%A A060354 Hareendra Yalamanchili (hyalaman(AT)mit.edu), Apr 01 2001

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