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A344504 a(n) = [x^n] ((x - 1)/sqrt(4/(x + 1) - 3) + x + 1)/(2*x*(3*x - 1)). 0
0, 1, 6, 26, 100, 361, 1254, 4245, 14108, 46247, 149998, 482412, 1540880, 4893859, 15468910, 48696930, 152764452, 477771447, 1490245302, 4637349186, 14400224496, 44632551567, 138101593398, 426658380621, 1316306945952, 4055853282741, 12482506508174, 38375733088400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Motzkin transform of the squares.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

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

a(n) ~ 4 * 3^(n - 1/2) * sqrt(n/Pi) * (1 - sqrt(3*Pi/n)/2). - Vaclav Kotesovec, May 24 2021

MAPLE

gf := ((x - 1)/sqrt(4/(x + 1) - 3) + x + 1)/(2*x*(3*x - 1)):

ser := series(gf, x, 30): seq(coeff(ser, x, n), n=0..27);

CROSSREFS

Cf. A064189 (Motzkin numbers).

Sequence in context: A234267 A055420 A137746 * A261064 A094811 A005022

Adjacent sequences:  A344501 A344502 A344503 * A344505 A344506 A344507

KEYWORD

nonn

AUTHOR

Peter Luschny, May 23 2021

STATUS

approved

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Last modified December 2 18:41 EST 2021. Contains 349445 sequences. (Running on oeis4.)