The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A336807 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A336807

a(n) = (n!)^2 * Sum_{k=0..n} 4^(n-k) / (k!)^2.
(history; published version)

#8 by Susanna Cuyler at Wed Jan 27 18:43:47 EST 2021

STATUS

proposed

approved

#7 by Ilya Gutkovskiy at Wed Jan 27 14:30:58 EST 2021

STATUS

editing

proposed

#6 by Ilya Gutkovskiy at Wed Jan 27 13:55:58 EST 2021

CROSSREFS

Cf. A006040, A056545, A336804, A336805, A336808.

#5 by Ilya Gutkovskiy at Wed Jan 27 13:48:38 EST 2021

NAME

allocated for Ilya Gutkovskiy

a(n) = (n!)^2 * Sum_{k=0..n} 4^(n-k) / (k!)^2.

DATA

1, 5, 81, 2917, 186689, 18668901, 2688321745, 526911062021, 134889231877377, 43704111128270149, 17481644451308059601, 8461115914433100846885, 4873602766713466087805761, 3294555470298303075356694437, 2582931488713869611079648438609, 2324638339842482649971683594748101

OFFSET

0,2

FORMULA

Sum_{n>=0} a(n) * x^n / (n!)^2 = BesselI(0,2*sqrt(x)) / (1 - 4*x).

a(0) = 1; a(n) = 4 * n^2 * a(n-1) + 1.

MATHEMATICA

Table[n!^2 Sum[4^(n - k)/k!^2, {k, 0, n}], {n, 0, 15}]

nmax = 15; CoefficientList[Series[BesselI[0, 2 Sqrt[x]]/(1 - 4 x), {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A006040, A056545.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Jan 27 2021

STATUS

approved

editing

#4 by Ilya Gutkovskiy at Wed Jan 27 13:48:38 EST 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#3 by R. J. Mathar at Tue Jan 26 10:42:20 EST 2021

STATUS

editing

approved

#2 by R. J. Mathar at Tue Jan 26 10:42:17 EST 2021

NAME

allocated for Christine Patterson

KEYWORD

allocated

recycled

STATUS

approved

editing

#1 by Christine Patterson at Tue Aug 04 15:26:17 EDT 2020

NAME

allocated for Christine Patterson

KEYWORD

allocated

STATUS

approved