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A144514
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a(n) = Sum_{k=0..n} (n+k+3)!/((n-k)!*k!*2^k).
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3
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6, 84, 1050, 13980, 205800, 3368316, 61075854, 1219445100, 26635157010, 632479986600, 16235529291696, 448220024574504, 13247429692101150, 417453231024613140, 13974133833217747650, 495278130521939366196, 18530507890959175097784, 729908595489477119015700
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OFFSET
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0,1
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LINKS
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FORMULA
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MAPLE
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f3:=proc(n) local k; add((n+k+3)!/((n-k)!*k!*2^k), k=0..n); end; [seq(f3(n), n=0..50)];
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MATHEMATICA
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Table[Sum[(n+k+3)!/((n-k)!k! 2^k), {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Jul 27 2019 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, (n+k+3)!/((n-k)!*k!*2^k))} \\ Seiichi Manyama, Apr 07 2019
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CROSSREFS
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Equals 6*A144506 (with a different offset).
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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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