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A275490 Square array of 5D pyramidal numbers, read by antidiagonals.

%I A275490 #16 Dec 05 2020 04:54:14
%S A275490 1,1,5,1,6,15,1,7,21,35,1,8,27,56,70,1,9,33,77,126,126,1,10,39,98,182,
%T A275490 252,210,1,11,45,119,238,378,462,330,1,12,51,140,294,504,714,792,495,
%U A275490 1,13,57,161,350,630,966,1254,1287,715,1,14,63,182,406,756,1218,1716,2079,2002,1001
%N A275490 Square array of 5D pyramidal numbers, read by antidiagonals.
%C A275490 Let F(r,n,d) = binomial(r+d-2,d-1)* ((r-1)*(n-2)+d) /d  be the d-dimensional pyramidal numbers. Then A(n,k) = F(k,n,5).
%C A275490 Sum of the n-th antidiagonal is binomial(n+4,7) + binomial(n+4,5) = A055797(n-1). - _Mathew Englander_, Oct 27 2020
%H A275490 Michael De Vlieger, <a href="/A275490/b275490.txt">Table of n, a(n) for n = 2..11176</a> (rows 2 <= n <= 150, flattened)
%H A275490 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to polygonal numbers</a>
%F A275490 A(n+2,k) = Sum_{j=0..k-1} A080852(n,j).
%F A275490 A(n,k) = binomial(k+3,4) + (n-2)*binomial(k+3,5). - _Mathew Englander_, Oct 27 2020
%e A275490 The array starts in rows n>=2 and columns k>=1 as
%e A275490    1    5   15   35   70  126  210  330  495   715  1001  1365  1820
%e A275490    1    6   21   56  126  252  462  792 1287  2002  3003  4368  6188
%e A275490    1    7   27   77  182  378  714 1254 2079  3289  5005  7371 10556
%e A275490    1    8   33   98  238  504  966 1716 2871  4576  7007 10374 14924
%e A275490    1    9   39  119  294  630 1218 2178 3663  5863  9009 13377 19292
%e A275490    1   10   45  140  350  756 1470 2640 4455  7150 11011 16380 23660
%e A275490    1   11   51  161  406  882 1722 3102 5247  8437 13013 19383 28028
%e A275490    1   12   57  182  462 1008 1974 3564 6039  9724 15015 22386 32396
%e A275490    1   13   63  203  518 1134 2226 4026 6831 11011 17017 25389 36764
%t A275490 Table[Binomial[k + 3, 4] + (# - 2)*Binomial[k + 3, 5] &[m - k + 1], {m, 2, 12}, {k, m - 1}] // Flatten (* _Michael De Vlieger_, Nov 05 2020 *)
%Y A275490 Cf. Row sums of A080852 (4D), A080851 (3D), A057145 (2D), A077028 (1D).
%Y A275490 Cf. A055797.
%K A275490 nonn,easy,tabl
%O A275490 2,3
%A A275490 _R. J. Mathar_, Jul 30 2016