The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A337826 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A337826

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

#4 by Susanna Cuyler at Thu Sep 24 14:00:08 EDT 2020

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Thu Sep 24 06:59:53 EDT 2020

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Thu Sep 24 06:24:47 EDT 2020

NAME

allocated for Ilya Gutkovskiy

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

DATA

1, 1, 10, 105, 2248, 62445, 2390436, 116650177, 7043659904, 514744959321, 44534754680500, 4493090921151261, 521600149636044480, 68900819660071184149, 10259571068808850618480, 1708054303772376318547125, 315688007001129064574027776, 64370788231256983836207599153

OFFSET

0,3

FORMULA

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

Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(Sum_{n>=1} n^3 * x^n / (n!)^2).

MATHEMATICA

a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k^4 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]

nmax = 17; CoefficientList[Series[Exp[x (BesselI[0, 2 Sqrt[x]] + Sqrt[x] BesselI[1, 2 Sqrt[x]])], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A023998, A279358, A336227, A337591, A337825.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Sep 24 2020

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Thu Sep 24 06:24:47 EDT 2020

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved