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A124920 Location of record values in A080577; also partial sums of A006128 plus 1.

%I A124920 #17 May 19 2018 12:35:50
%S A124920 1,2,5,11,23,43,78,132,218,346,538,813,1212,1768,2548,3616,5079,7044,
%T A124920 9688,13186,17816,23868,31767,41973,55147,71998,93520,120814,155359,
%U A124920 198812,253375,321510,406437,511803,642265,803141,1001155,1243967
%N A124920 Location of record values in A080577; also partial sums of A006128 plus 1.
%H A124920 Vaclav Kotesovec, <a href="/A124920/b124920.txt">Table of n, a(n) for n = 1..10000</a>
%F A124920 A124920(n) = A124920(n-1)+ A006128(n-1), n>1; a(1) = 1.
%F A124920 G.f.: x/(1 - x) + Sum_{i>=1} i*x^(i+1)/(1 - x) * Product_{j=1..i} 1/(1 - x^j). - _Ilya Gutkovskiy_, Apr 04 2017
%F A124920 a(n) ~ exp(Pi*sqrt(2*n/3)) * (log(6*n) + 2*gamma - 2*log(Pi)) * sqrt(3) / (4*Pi^2), where gamma is the Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, May 19 2018
%e A124920 A080577 begins
%e A124920 1
%e A124920 2 11
%e A124920 3 21 111
%e A124920 4 31 22 211 1111
%e A124920 5 41 32 311 221 2111 11111
%e A124920 6 51 42 411 33 321 3111 222 2211 21111 111111
%e A124920 therefore A124920 begins 1 2 5 11 23 ...
%p A124920 A008284 := proc(n,k) if n >= 1 and n = k or k = 1 then 1 elif k > n then 0 else add( A008284(n-k,i),i=1..k) ; fi ; end: A006128 := proc(n) add( k*A008284(n,k),k=1..n) ; end: a := 1 : printf("%d,",a) ; for n from 2 to 80 do a := a + A006128(n-1) : printf("%d,",a) ; od : # _R. J. Mathar_, Jan 13 2007
%Y A124920 Cf. A000041, A006128, A080577.
%K A124920 easy,nonn
%O A124920 1,2
%A A124920 _Alford Arnold_, Nov 13 2006
%E A124920 More terms from _R. J. Mathar_, Jan 13 2007
%E A124920 Clarification of name from _Ilya Gutkovskiy_, Apr 04 2017