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A045894 4-fold convolution of A001700(n), n >= 0. 5
1, 12, 94, 608, 3525, 19044, 97954, 486000, 2345930, 11081880, 51447036, 235454848, 1064832173, 4767347796, 21160397050, 93223960784, 408037319262, 1775744775592, 7688699122724, 33140226601920, 142262721338146 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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.
Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
FORMULA
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.
MATHEMATICA
Table[(n + 11)*4^(n + 2) - (n + 5) Binomial[2 (n + 4), n + 4]/2, {n, 0, 20}] (* Michael De Vlieger, Feb 18 2017 *)
PROG
(Python)
import math
def C(n, r):
....f=math.factorial
....return f(n)/f(r)/f(n-r)
def A045894(n):
....return (n+11)*4**(n+2)-(n+5)*C(2*(n+4), (n+4))/2 # Indranil Ghosh, Feb 18 2017
CROSSREFS
Sequence in context: A294449 A073913 A057410 * A045829 A220683 A009647
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified February 26 11:31 EST 2024. Contains 370352 sequences. (Running on oeis4.)