A364924
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - 2*x*A(x)^4).
Original entry on oeis.org
1, 1, 7, 67, 743, 8970, 114445, 1517976, 20722023, 289224355, 4108588558, 59207805442, 863439906413, 12718638581368, 188960182480440, 2828238875318256, 42605850936335463, 645497106959662857, 9829072480785776101, 150345303724987825021
Offset: 0
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a(n) = sum(k=0, n, 3^k*(-2)^(n-k)*binomial(n, k)*binomial(4*n+k+1, n)/(4*n+k+1));
A243693
Number of Hyposylvester classes of 3-multiparking functions of length n.
Original entry on oeis.org
1, 1, 5, 32, 233, 1833, 15180, 130392, 1151057, 10378883, 95182445, 885053524, 8324942620, 79071217228, 757310811912, 7305728683824, 70923966744609, 692370887676567, 6792525607165935, 66933512163735000, 662190712902022017, 6574831459429388169, 65494637699437417584
Offset: 0
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a := proc(n) option remember; if n <= 1 then return 1 fi;
(a(n - 2)*(-800*n^3 + 3024*n^2 - 3184*n + 672) + a(n - 1)*(3275*n^3 - 7467*n^2 +
5038*n - 1008))/(300*n^3 - 234*n^2 - 192*n) end:
seq(a(n), n = 0..22); # Peter Luschny, Apr 13 2024
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a[n_] := 3^(n - Boole[n>0]) Hypergeometric2F1[1 - n, -2 n, 2, 1/3];
Table[a[n], {n, 0, 22}] (* Peter Luschny, Apr 12 2024 *)
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a(n) = sum(k=0, n, 3^k*(-2)^(n-k)*binomial(n, k)*binomial(2*n+k+1, n)/(2*n+k+1)); \\ Seiichi Manyama, Aug 12 2023
Name clarified by
Jun Yan, Apr 12 2024
A371405
Expansion of (1/x) * Series_Reversion( x / ( (1+x) * (1+3*x)^3 ) ).
Original entry on oeis.org
1, 10, 136, 2134, 36379, 654670, 12239560, 235407070, 4627854244, 92576970280, 1878395043232, 38564373070090, 799651963174978, 16722655896174004, 352289843771100400, 7469327989417602862, 159263992188702829900, 3412969567344634872952
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+3*x)^3))/x)
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a(n) = sum(k=0, n, 3^k*binomial(3*(n+1), k)*binomial(n+1, n-k))/(n+1);
Showing 1-3 of 3 results.