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%I #17 Oct 06 2021 12:56:48
%S 1,8,31,80,160,272,416,592,800,1040,1312,1616,1952,2320,2720,3152,
%T 3616,4112,4640,5200,5792,6416,7072,7760,8480,9232,10016,10832,11680,
%U 12560,13472,14416,15392,16400,17440,18512,19616,20752,21920,23120,24352
%N Row sums of correlation triangle for (1+x)^3/(1-x).
%C Row sums of number triangle A115292.
%C If Y_i (i=1,2,3,4,5) are 2-blocks of a (n+5)-set X then a(n-2) is the number of 7-subsets of X intersecting each Y_i (i=1,2,3,4,5). - _Milan Janjic_, Oct 28 2007
%H Michael De Vlieger, <a href="/A115293/b115293.txt">Table of n, a(n) for n = 0..10000</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: A(x) = (1+x)^5/(1-x)^3.
%F a(n) = Sum_{k = 0..n} Sum_{j = 0..n} [j<=k]*A115291(k-j)*[j<=n-k]*A115291(n-k-j).
%F From _Peter Bala_, Sep 26 2021: (Start)
%F a(n) = Sum_{k = 0..n} binomial(5,n-k)*binomial(k+2,k).
%F A262732(n) = [x^n] A(x)^n. (End)
%p seq(add(binomial(5,n-k)*binomial(k+2,k), k = 0..n), n = 0..40); # _Peter Bala_, Sep 26 2021
%t LinearRecurrence[{3,-3,1},{1,8,31,80,160,272},50] (* _Harvey P. Dale_, Dec 03 2018 *)
%o (PARI) a(n) = sum(k = 0, n, binomial(5,n-k)*binomial(k+2,k)); \\ _Michel Marcus_, Oct 01 2021
%Y Cf. A115291, A115292, A262732.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Jan 19 2006
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