The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A337824 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A337824

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

#11 by OEIS Server at Sun Jan 07 01:49:30 EST 2024

LINKS

Robert Israel, <a href="/A337824/b337824_1.txt">Table of n, a(n) for n = 0..257</a>

#10 by Michel Marcus at Sun Jan 07 01:49:30 EST 2024

STATUS

reviewed

approved

Discussion

Sun Jan 07

01:49

OEIS Server: Installed first b-file as b337824.txt.

#9 by Joerg Arndt at Sun Jan 07 00:55:08 EST 2024

STATUS

proposed

reviewed

#8 by Robert Israel at Sun Jan 07 00:43:13 EST 2024

STATUS

editing

proposed

#7 by Robert Israel at Sun Jan 07 00:43:08 EST 2024

LINKS

Robert Israel, <a href="/A337824/b337824_1.txt">Table of n, a(n) for n = 0..257</a>

MAPLE

S:= series(log(1+x*BesselI(0, 2*sqrt(x))), x, 31):

0, seq(coeff(S, x, n)*(n!)^2, n=1..30); # Robert Israel, Jan 07 2024

STATUS

approved

editing

#6 by Susanna Cuyler at Thu Sep 24 13:59:44 EDT 2020

STATUS

proposed

approved

#5 by Ilya Gutkovskiy at Thu Sep 24 06:59:58 EDT 2020

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Thu Sep 24 06:50:06 EDT 2020

CROSSREFS

Cf. A002190, A101981, A033464, A101981, A337590, A337591, A337825.

#3 by Ilya Gutkovskiy at Thu Sep 24 06:29:52 EDT 2020

CROSSREFS

Cf. A002190, A101981, A033464, A337590, A337591, A337825.

#2 by Ilya Gutkovskiy at Thu Sep 24 06:17:00 EDT 2020

NAME

allocated for Ilya Gutkovskiy

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

DATA

0, 1, 2, -15, 16, 2505, -60264, -606515, 131316928, -4813100271, -339213768200, 62401665573621, -2075963863814928, -745086903175541927, 140250562903680456332, 808225064553580739325, -5491409141464496462591744, 1013058261721909845376508449, 127689148764914765889971316600

OFFSET

0,3

FORMULA

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

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

MATHEMATICA

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

nmax = 18; CoefficientList[Series[Log[1 + x BesselI[0, 2 Sqrt[x]]], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A002190, A101981, A033464, A337590, A337591.

KEYWORD

allocated

sign

AUTHOR

Ilya Gutkovskiy, Sep 24 2020

STATUS

approved

editing