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A351726 Table T(n,k) read by rows: number of compositions of n into k parts of size 1, 5, 10 or 25.

%I A351726 #13 Feb 17 2022 11:40:28
%S A351726 1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,1,0,0,0,1,0,0,2,0,0,0,1,0,0,0,3,0,0,
%T A351726 0,1,0,0,0,0,4,0,0,0,1,0,0,0,0,0,5,0,0,0,1,0,1,1,0,0,0,6,0,0,0,1,0,0,
%U A351726 2,3,0,0,0,7,0,0,0,1,0,0,0,3,6,0,0,0,8,0,0,0,1,0,0,0,0,4
%N A351726 Table T(n,k) read by rows: number of compositions of n into k parts of size 1, 5, 10 or 25.
%H A351726 L. Zhiwen, <a href="https://math.stackexchange.com/questions/4380108/expect-coin-value-probelm-a-variant-of-coin-change-problem">Expect coin value problem (a variant of coin exchange problem)</a>, math.stackexchange Feb 12, 2022.
%H A351726 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%F A351726 T(n,0) = 0 if k>0.
%F A351726 G.f.: 1/(1-y*g(x)) where g(x)=x+x^5+x^10+x^25 is the g.f. of column k=1.
%e A351726 T(7,3)=3 counts 1+1+5 =1+5+1 =5+1+1.
%e A351726 T(10,2)=1 counts 5+5.
%e A351726 T(12,3)=3 counts 1+1+10 =1+10+1 =10+1+1.
%e A351726 T(15,3)=1 counts 5+5+5.
%e A351726 T(16,3)=6 counts 1+5+10 =1+10+5 =5+1+10 =5+10+1 =10+1+5 =10+5+1.
%e A351726 The triangle starts in row n=0 and columns 0<=k<=n:
%e A351726 1
%e A351726 0 1
%e A351726 0 0 1
%e A351726 0 0 0 1
%e A351726 0 0 0 0  1
%e A351726 0 1 0 0  0  1
%e A351726 0 0 2 0  0  0  1
%e A351726 0 0 0 3  0  0  0  1
%e A351726 0 0 0 0  4  0  0  0  1
%e A351726 0 0 0 0  0  5  0  0  0  1
%e A351726 0 1 1 0  0  0  6  0  0  0   1
%e A351726 0 0 2 3  0  0  0  7  0  0   0  1
%e A351726 0 0 0 3  6  0  0  0  8  0   0  0  1
%e A351726 0 0 0 0  4 10  0  0  0  9   0  0  0  1
%e A351726 0 0 0 0  0  5 15  0  0  0  10  0  0  0  1
%e A351726 0 0 2 1  0  0  6 21  0  0   0 11  0  0  0  1
%e A351726 0 0 0 6  4  0  0  7 28  0   0  0 12  0  0  0  1
%e A351726 0 0 0 0 12 10  0  0  8 36   0  0  0 13  0  0  0  1
%e A351726 0 0 0 0  0 20 20  0  0  9  45  0  0  0 14  0  0  0 1
%e A351726 0 0 0 0  0  0 30 35  0  0  10 55  0  0  0 15  0  0 0 1
%e A351726 0 0 1 3  1  0  0 42 56  0   0 11 66  0  0  0 16  0 0 0 1
%e A351726 0 0 0 3 12  5  0  0 56 84   0  0 12 78  0  0  0 17 0 0 0 1
%e A351726 0 0 0 0  6 30 15  0  0 72 120  0  0 13 91  0  0  0 18 0 0 0 1
%Y A351726 Cf. A351724 (row sums), A351725 (partitions).
%K A351726 nonn,easy,tabl
%O A351726 0,24
%A A351726 _R. J. Mathar_, Feb 17 2022