The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372018

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A372018

G.f. A(x) satisfies A(x) = ( 1 + 4*x*A(x)/(1 - x*A(x)) )^(1/2).
(history; published version)

#12 by R. J. Mathar at Mon Apr 22 12:45:55 EDT 2024

STATUS

editing

approved

#11 by R. J. Mathar at Mon Apr 22 12:45:48 EDT 2024

FORMULA

D-finite with recurrence n*(n+1)*(n-2)*a(n) -6*(n-2)*(3*n^2-6*n+1)*a(n-2) -27*n*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Apr 22 2024

Conjecture: a(2n+1) = 2*A371364(). - R. J. Mathar, Apr 22 2024

MAPLE

A372018 := proc(n)

add(4^k*binomial((n+1)/2, k)*binomial(n-1, k-1), k=0..n) ;

%/(n+1) ;

end proc:

seq(A372018(n), n=0..60) ; # R. J. Mathar, Apr 22 2024

STATUS

approved

editing

#10 by Michael De Vlieger at Tue Apr 16 10:26:35 EDT 2024

STATUS

reviewed

approved

#9 by Joerg Arndt at Tue Apr 16 10:12:12 EDT 2024

STATUS

proposed

reviewed

#8 by Seiichi Manyama at Tue Apr 16 07:20:08 EDT 2024

STATUS

editing

proposed

#7 by Seiichi Manyama at Tue Apr 16 00:03:24 EDT 2024

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(n/2+1/2,k) * binomial(n-1,n-k).

#6 by Seiichi Manyama at Tue Apr 16 00:00:39 EDT 2024

CROSSREFS

Cf. A372019, A372020.

#5 by Seiichi Manyama at Mon Apr 15 23:57:10 EDT 2024

DATA

1, 2, 4, 10, 30, 98, 336, 1194, 4360, 16258, 61644, 236938, 921102, 3615330, 14307312, 57024426, 228701646, 922283522, 3737497980, 15212318730, 62160993642, 254909413218, 1048717979424, 4327273358250, 17903826642780, 74260741616514, 308724721176676

#4 by Seiichi Manyama at Mon Apr 15 23:56:27 EDT 2024

DATA

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 26843545610, 30, 98, 336, 1194, 4360, 16258, 61644, 236938, 921102, 3615330, 14307312, 57024426, 228701646, 922283522, 3737497980, 15212318730, 62160993642, 254909413218

#3 by Seiichi Manyama at Mon Apr 15 23:56:03 EDT 2024

FORMULA

a(n) = (1/(n+1)) * Sum_{k=0..n}4^k * binomial(n/2+1/2,k) * binomial(n-1,n-k).

PROG

(PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+1/2, k)*binomial(n-1, n-k))/(n+1);