A162013 The sequence of the absolute values of the a(n-3) coefficients of A162011.

0, 9, 3748, 163160, 2549775, 22768402, 141820764, 685234196, 2738273230, 9438613635, 28894483904, 80240970524, 205377597269, 490460693060, 1103418293480, 2356809738456, 4809498575164, 9426116131517, 17820475867500

Offset: 1

Author

Johannes W. Meijer, Jun 27 2009

Keywords

• easy
• nonn

Crossrefs

Equals the absolute values of the coefficients that precede the a(n-3) factors of the recurrence relations RR(n) of A162011.

Cf. A006324 [a(n-1)] and A162012 [a(n-2)].

Programs

Maple

nmax:=21; for n from 1 to nmax do RR(n) := expand(product((1-(2*k-1)^2*z)^(n-k+1),k=1..n),z) od: T:=1: for n from 1 to nmax do a(T):=coeff(-RR(n),z,3): T:=T+1 od: seq(a(k),k=1..T-1);

Formula

a(n) = (280*n^12+1680*n^11-252*n^10-16660*n^9-13758*n^8+63408*n^7+68705*n^6-104265*n^5-111657*n^4+66997*n^3+56682*n^2-11160*n)/45360

Recurrence relation sum((-1)^k*binomial(13,k)*a(n-k), k= 0..13) = 0

GF(z) = z*(9+3631*z+115138*z^2+718465*z^3+1282314*z^4+718465*z^5+115138*z^6+ 3631*z^7+ 9*z^8)/(1-z)^13