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A000751 Boustrophedon transform of partition numbers.

%I A000751 #34 Jun 12 2022 12:01:07
%S A000751 1,2,5,14,42,143,555,2485,12649,72463,461207,3229622,24671899,
%T A000751 204185616,1819837153,17378165240,177012514388,1915724368181,
%U A000751 21952583954117,265533531724484,3380877926676504,45199008472762756
%N A000751 Boustrophedon transform of partition numbers.
%H A000751 John Cerkan, <a href="/A000751/b000751.txt">Table of n, a(n) for n = 0..482</a>
%H A000751 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%H A000751 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996) 44-54 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H A000751 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A000751 Wikipedia, <a href="http://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon_transform</a>
%H A000751 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A000751 a(n) = Sum_{k=0..n} A109449(n,k)*A000041(k). - _Reinhard Zumkeller_, Nov 03 2013
%e A000751 The array begins:
%e A000751                    1
%e A000751                1  ->   2
%e A000751            5  <-   4  <-   2
%e A000751        3  ->   8  ->  12  ->  14
%e A000751   42  <-  39  <-  31  <-  19  <-   5
%e A000751 - _John Cerkan_, Jan 26 2017
%t A000751 t[n_, 0] := PartitionsP[n]; t[n_, k_] := t[n, k] = t[n, k - 1] + t[n - 1, n - k]; a[n_] := t[n, n]; Array[a, 30, 0] (* _Jean-François Alcover_, Feb 12 2016 *)
%o A000751 (Haskell)
%o A000751 a000751 n = sum $ zipWith (*) (a109449_row n) a000041_list
%o A000751 -- _Reinhard Zumkeller_, Nov 03 2013
%o A000751 (Python)
%o A000751 from itertools import accumulate, count, islice
%o A000751 from sympy import npartitions
%o A000751 def A000751_gen(): # generator of terms
%o A000751     blist = tuple()
%o A000751     for i in count(0):
%o A000751         yield (blist := tuple(accumulate(reversed(blist),initial=npartitions(i))))[-1]
%o A000751 A000751_list = list(islice(A000751_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A000751 Cf. A000733, A230957.
%K A000751 nonn
%O A000751 0,2
%A A000751 _N. J. A. Sloane_