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URL: https://oeis.org/A365760

⇱ A365760 - OEIS

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A365760
G.f. A(x) satisfies A(x) = 1 + x*A(x)*(1 + x^4*A(x)^5).
5
1, 1, 1, 1, 1, 2, 8, 29, 85, 211, 469, 1003, 2263, 5734, 15926, 45188, 124730, 330583, 850783, 2175406, 5650746, 15064128, 41006034, 112492472, 307511726, 833907512, 2247908392, 6056190352, 16390505332, 44659671982, 122380777306, 336326321179, 924529751087
OFFSET
0,6
FORMULA
a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k,k) * binomial(n+k+1,n-4*k) / (n+k+1) = Sum_{k=0..floor(n/5)} binomial(n+k,6*k) * binomial(6*k,k) / (5*k+1).
G.f.: (1/x) * Series_Reversion( x * (1 - x^5) / (1 + x) ). - Seiichi Manyama, Oct 04 2025
PROG
(PARI) a(n) = sum(k=0, n\5, binomial(n-4*k, k)*binomial(n+k+1, n-4*k)/(n+k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 18 2023
STATUS
approved