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A045894
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4-fold convolution of A001700(n), n >= 0.
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5
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1, 12, 94, 608, 3525, 19044, 97954, 486000, 2345930, 11081880, 51447036, 235454848, 1064832173, 4767347796, 21160397050, 93223960784, 408037319262, 1775744775592, 7688699122724, 33140226601920, 142262721338146
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OFFSET
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0,2
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LINKS
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José Agapito, Ângela Mestre, Maria M. Torres, and Pasquale Petrullo, On One-Parameter Catalan Arrays, Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.1.
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FORMULA
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a(n) = (n+11)*4^(n+2) - (n+5)*binomial(2*(n+4), n+4)/2;
G.f.: c(x)^4/(1-4*x)^2, where c(x) = g.f. for Catalan numbers A000108;
recursion: a(n)= (2*(2*n+10)/(n+4))*a(n-1) + (4/(n+4))*A045720(n), a(0)=1.
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MATHEMATICA
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Table[(n + 11)*4^(n + 2) - (n + 5) Binomial[2 (n + 4), n + 4]/2, {n, 0, 20}] (* Michael De Vlieger, Feb 18 2017 *)
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PROG
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(Python)
import math
def C(n, r):
....f=math.factorial
....return f(n)/f(r)/f(n-r)
....return (n+11)*4**(n+2)-(n+5)*C(2*(n+4), (n+4))/2 # Indranil Ghosh, Feb 18 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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