The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A119243

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A119243

Eigenvector of triangle A118919, so that a(n) = Sum_{k=0..floor(n/2)} A118919(n,k)*a(k).
(history; published version)

#13 by OEIS Server at Tue Sep 19 15:32:00 EDT 2023

LINKS

Andrew Howroyd, <a href="/A119243/b119243_1.txt">Table of n, a(n) for n = 0..1000</a>

#12 by Michael De Vlieger at Tue Sep 19 15:32:00 EDT 2023

STATUS

reviewed

approved

Discussion

Tue Sep 19

15:32

OEIS Server: Installed first b-file as b119243.txt.

#11 by Peter Luschny at Tue Sep 19 13:24:16 EDT 2023

STATUS

proposed

reviewed

#10 by Michel Marcus at Tue Sep 19 12:12:35 EDT 2023

STATUS

editing

proposed

#9 by Michel Marcus at Tue Sep 19 12:12:22 EDT 2023

CROSSREFS

Cf. A118919, A119244 (A(x)^(1/2)), A119245.

STATUS

proposed

editing

#8 by Andrew Howroyd at Tue Sep 19 11:16:43 EDT 2023

STATUS

editing

proposed

#7 by Andrew Howroyd at Tue Sep 19 11:15:58 EDT 2023

NAME

Eigenvector of triangle A118919, so that a(n) = Sum_{k=0..[floor(n\/2])} A118919(n,k)*a(k).

LINKS

Andrew Howroyd, <a href="/A119243/b119243_1.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

G.f. A(x) satisfies: A(x) = A(-x/(1-4*x))/(1-4*x).

G.f. A(x) satisfies: A(x) = A(-x/(1-4*x))/(1-4*x). Eigenvector: a(n) = Sum_{k=0..[floor(n\/2])} a(k)*(2*k+1)*Cbinomial(2*n+2,n-2*k)/(n+1) for n>=0, with a(0)=1.

PROG

(PARI) seq(n) = {my(a=vector(n+1)); a[1]=1; for(n=1, n, a[1+n] = sum(k=0, n\2, a[1+k]*(2*k+1)*binomial(2*n+2, n-2*k))/(n+1)); a} \\ Andrew Howroyd, Sep 19 2023

STATUS

proposed

editing

#6 by Peter Bala at Tue Sep 19 08:38:32 EDT 2023

STATUS

editing

proposed

#5 by Peter Bala at Tue Sep 19 06:26:22 EDT 2023

FORMULA

Apparently, It appears that the g.f. A(x) satisfies A(x^2) = 1/(1 + x)^2*A(x/(1 + x)^2). - Peter Bala, Sep 16 2023

#4 by Peter Bala at Sat Sep 16 16:45:54 EDT 2023

FORMULA

Apparently, the g.f. A(x) satisfies A(x^2) = 1/(1 + x)^2*A(x/(1 + x)^2). - Peter Bala, Sep 16 2023

STATUS

approved

editing