Search: a364589 -id:a364589
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A364590
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G.f. satisfies A(x) = 1/(1-x) + x^4*A(x)^3.
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+10
2
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1, 1, 1, 1, 2, 4, 7, 11, 19, 37, 74, 142, 268, 518, 1033, 2077, 4152, 8290, 16687, 33899, 69148, 141160, 288650, 592354, 1220086, 2519226, 5210164, 10794088, 22408556, 46613554, 97125751, 202662419, 423459427, 886048249, 1856448852, 3894362560, 8178530890
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/4)} binomial(n-2*k,2*k) * binomial(3*k,k) / (2*k+1).
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PROG
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(PARI) a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k)*binomial(3*k, k)/(2*k+1));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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A369691
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G.f. satisfies A(x) = 1/(1-x)^3 + x^3*A(x)^3.
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+10
1
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1, 3, 6, 11, 24, 66, 196, 576, 1692, 5110, 15933, 50604, 161988, 521700, 1693362, 5541679, 18260055, 60487659, 201272437, 672550158, 2256204327, 7596059333, 25655943417, 86904524289, 295154911774, 1004906765178, 3429178160346, 11726499288028, 40178538608682
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/3)} binomial(n+3*k+2,n-3*k) * binomial(3*k,k) / (2*k+1).
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PROG
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(PARI) a(n) = sum(k=0, n\3, binomial(n+3*k+2, n-3*k)*binomial(3*k, k)/(2*k+1));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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