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A000733 Boustrophedon transform of partition numbers 1, 1, 1, 2, 3, 5, 7, ...

%I A000733 #45 Jun 13 2022 03:02:52
%S A000733 1,2,4,10,30,101,394,1760,8970,51368,326991,2289669,17491625,
%T A000733 144760655,1290204758,12320541392,125496010615,1358185050788,
%U A000733 15563654383395,188254471337718,2396930376564860,32044598671291610
%N A000733 Boustrophedon transform of partition numbers 1, 1, 1, 2, 3, 5, 7, ...
%H A000733 John Cerkan, <a href="/A000733/b000733.txt">Table of n, a(n) for n = 0..482</a>
%H A000733 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.
%H A000733 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 A000733 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H A000733 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H A000733 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%e A000733 The array begins:
%e A000733                    1
%e A000733                1  ->   2
%e A000733            4  <-   3  <-   1
%e A000733        2  ->   6  ->   9  ->  10
%e A000733   30  <-  28  <-  22  <-  13  <-   3
%e A000733 - _John Cerkan_, Jan 26 2017
%t A000733 t[n_, 0] := If[n == 0, 1, PartitionsP[n-1]]; 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 A000733 (Haskell)
%o A000733 a000733 n = sum $ zipWith (*) (a109449_row n) (1 : a000041_list)
%o A000733 -- _Reinhard Zumkeller_, Nov 04 2013
%o A000733 (Python)
%o A000733 from itertools import count, accumulate, islice
%o A000733 from sympy import npartitions
%o A000733 def A000733_gen(): # generator of terms
%o A000733     yield 1
%o A000733     blist = (1,)
%o A000733     for i in count(0):
%o A000733         yield (blist := tuple(accumulate(reversed(blist),initial=npartitions(i))))[-1]
%o A000733 A000733_list = list(islice(A000733_gen(),40)) # _Chai Wah Wu_, Jun 12 2022
%Y A000733 Cf. A000041, A000751, A109449, A230957.
%K A000733 nonn
%O A000733 0,2
%A A000733 _N. J. A. Sloane_, _Simon Plouffe_