1,2

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).

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.

Rows 1 thru 20 and 22 thru 25 are as follows:

A000012 A008619 A000027 A001399 A002620 A001400 A000217 A006918 A000601 A001401 A002623 A001402 A002621 A097701 A000292 A008630 A002624 A008631 A057524 A002622 A008632 A001752 A117485.

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]

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]

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]

Sequence in context: A002797 A062492 A165271 this_sequence A093694 A068006 A000097

Adjacent sequences: A139669 A139670 A139671 this_sequence A139673 A139674 A139675

nonn

Alford Arnold (Alford1940(AT)aol.com), Apr 29 2008, May 01 2008

More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Nov 10 2008

Corrected A-number in definition. Added formula. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 21 2008