The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A307755

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A307755

Exponential convolution of partition numbers (A000041) with themselves.
(history; published version)

#12 by Vaclav Kotesovec at Mon May 06 10:00:17 EDT 2019

STATUS

editing

approved

#11 by Vaclav Kotesovec at Mon May 06 10:00:12 EDT 2019

FORMULA

a(n) ~ exp(2*Pi*sqrt(n/3)) * 2^(n-2) / (3*n^2). - Vaclav Kotesovec, May 06 2019

#10 by Vaclav Kotesovec at Mon May 06 08:34:57 EDT 2019

LINKS

Vaclav Kotesovec, <a href="/A307755/b307755.txt">Table of n, a(n) for n = 0..3000</a>

STATUS

approved

editing

#9 by Alois P. Heinz at Fri Apr 26 19:38:02 EDT 2019

STATUS

editing

approved

#8 by Alois P. Heinz at Fri Apr 26 19:37:13 EDT 2019

MAPLE

a:= n-> (p-> add(binomial(n, j)*p(j)*p(n-j), j=0..n))(combinat[numbpart]):

seq(a(n), n=0..30); # Alois P. Heinz, Apr 26 2019

STATUS

proposed

editing

#7 by Ilya Gutkovskiy at Fri Apr 26 19:31:30 EDT 2019

STATUS

editing

proposed

#6 by Ilya Gutkovskiy at Fri Apr 26 19:30:14 EDT 2019

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k)*A000041(k)*A000041(n-k).

STATUS

proposed

editing

#5 by Ilya Gutkovskiy at Fri Apr 26 19:09:56 EDT 2019

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Fri Apr 26 18:57:13 EDT 2019

CROSSREFS

Cf. A000041, A000712, A218481, A307756.

#3 by Ilya Gutkovskiy at Fri Apr 26 18:52:44 EDT 2019

NAME

allocated for Ilya GutkovskiyExponential convolution of partition numbers (A000041) with themselves.

DATA

1, 2, 6, 18, 58, 184, 586, 1822, 5618, 16980, 50892, 150064, 439210, 1268924, 3640342, 10337596, 29160638, 81570368, 226795202, 626070664, 1718783084, 4689582366, 12730998988, 34373603158, 92385339242, 247099560046, 658137847408, 1745322097886, 4610549234836, 12131656526628

OFFSET

0,2

FORMULA

E.g.f.: (Sum_{k>=0} A000041(k)*x^k/k!)^2.

a(n) = binomial(n,k)*A000041(k)*A000041(n-k).

MATHEMATICA

nmax = 29; CoefficientList[Series[Sum[PartitionsP[k] x^k/k!, {k, 0, nmax}]^2, {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[Binomial[n, k] PartitionsP[k] PartitionsP[n - k], {k, 0, n}], {n, 0, 29}]

CROSSREFS

Cf. A000041, A000712, A218481.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Apr 26 2019

STATUS

approved

editing