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A365753
Expansion of (1/x) * Series_Reversion( x*(1+x)*(1-x)^5 ).
7
1, 4, 27, 220, 1984, 19064, 191325, 1981932, 21031965, 227463808, 2498039219, 27782561352, 312281382836, 3541879743840, 40484779373060, 465888833819532, 5393215780225983, 62761359573224612, 733784067570047400, 8615217370731224160, 101533102164551821896
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} (-1)^k * binomial(n+k,k) * binomial(6*n-k+4,n-k).
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(5*n-2*k+3,n-2*k). - Seiichi Manyama, Jan 18 2024
a(n) = (1/(n+1)) * [x^n] 1/( (1+x) * (1-x)^5 )^(n+1). - Seiichi Manyama, Feb 16 2024
PROG
(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(6*n-k+4, n-k))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 18 2023
STATUS
approved