%I A139672
%S A139672 1,2,5,9,17,27,44,65,97,136,191,257,346,451,587,746,946,1177,1461,1786,
%T A139672 2178,2623,3151,3746,4443,5223,6126,7131,8283,9558,11007,12603,14403,
%U A139672 16377,18588,21003,23692,26618,29858,33372,37244,41430,46022,50972
%N A139672 Convolution of A008619 and A001400.
%C A139672 This is row 21 of a table of values related to Molien series. It is the 
               product of the sequence on row 3 (A008619) with the sequence on row 
               7 (A001400).
%C A139672 This table may be constructed by moving the rows of table A008284 to 
               prime locations and generating the composite locations by multiplication 
               in a manner similar to the calculation illustrated in the present 
               sequence.
%C A139672 Rows 1 thru 20 and 22 thru 25 are as follows:
%C A139672 A000012 A008619 A000027 A001399 A002620 A001400 A000217 A006918 A000601 
               A001401 A002623 A001402 A002621 A097701 A000292 A008630 A002624 A008631 
               A057524 A002622 A008632 A001752 A117485.
%F A139672 G.f.: x/((x^2+x+1)*(x^2+1)*(x+1)^3*(x-1)^6). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), 
               Nov 10 2008]
%F A139672 a(n)= -A049347(n)/27 +(2*n+11)*(6*n^4+132*n^3+914*n^2+2068*n+1055)/69120 
               -(-1)^n*(51/512+n^2/256+11*n/256+A057077(n)/32 ) . [From R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Nov 21 2008]
%p A139672 a:= proc(n) local m, r; m:= iquo (n, 12, 'r'); r:= r+1; (19+ (145+ (260+ 
               15* (r+9)*r+ (405+ 90*r+ 216*m) *m) *m) *m) *m/5+ [0, 1, 2, 5, 9, 
               17, 27, 44, 65, 97, 136, 191][r]+ [0, 16, 37, 77, 128, 208, 307, 
               447, 616, 840, 1105, 1441][r]*m/2+ [0, 52, 119, 213, 328, 476, 651, 
               865, 1112, 1404, 1735, 2117][r]*m^2/2 end: seq (a(n), n=1..50); [From 
               Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 10 2008]
%Y A139672 Sequence in context: A002797 A062492 A165271 this_sequence A093694 A068006 
               A000097
%Y A139672 Adjacent sequences: A139669 A139670 A139671 this_sequence A139673 A139674 
               A139675
%K A139672 nonn
%O A139672 1,2
%A A139672 Alford Arnold (Alford1940(AT)aol.com), Apr 29 2008, May 01 2008
%E A139672 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 10 2008
%E A139672 Corrected A-number in definition. Added formula. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 21 2008