The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A337591 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A337591

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k^3 * a(n-k).
(history; published version)

#4 by Susanna Cuyler at Wed Sep 02 19:24:20 EDT 2020

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Wed Sep 02 09:09:32 EDT 2020

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Wed Sep 02 08:03:15 EDT 2020

NAME

allocated for Ilya Gutkovskiy

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k^3 * a(n-k).

DATA

1, 1, 6, 51, 760, 15545, 428256, 15043483, 653049664, 34204348305, 2118834917200, 152834879685851, 12670536337934256, 1194143629239156505, 126753440317516749660, 15031687739886065433375, 1977667235694725269563136, 286890421090357737699794209, 45637300134026406622214264592

OFFSET

0,3

FORMULA

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

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

MATHEMATICA

a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k^3 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

nmax = 18; CoefficientList[Series[Exp[x BesselI[0, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A033462, A336227.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Sep 02 2020

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Wed Sep 02 08:03:15 EDT 2020

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved