A395669 - OEIS

A395669

Expansion of g^7*(4-3*g)/(7-6*g)^2, where g = 1+x*g^7 is the g.f. of A002296.

1, 16, 268, 4572, 78746, 1364104, 23719728, 413545356, 7224055351, 126380687416, 2213511996356, 38804671881288, 680789488507506, 11951216432486432, 209912513875637888, 3688563381314685804, 64839772922717680659, 1140167947961926829368, 20054925618261969731104

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

FORMULA

Sum_{k>=1} a(k-1) * x^k/k = (1/14) * log( Sum_{k>=0} binomial(7*k+7,k) * x^k ).

a(n) = A395667(n)/(n+1) = (1/14) * (binomial(7*n+6,n) + Sum_{k=0..n+1} 6^(n+1-k) * binomial(7*n+7,k)).

a(n) = (1/12) * Sum_{k=0..n+1} 6^(n+1-k) * binomial(7*n+6,k).

a(n) = (1/(n+1)) * Sum_{k=0..n} 6^k * binomial(k+2,2) * binomial(7*n+7,n-k).

PROG

(PARI) a(n) = (binomial(7*n+6, n)+sum(k=0, n+1, 6^(n+1-k)*binomial(7*n+7, k)))/14;