This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A071976 #29 Apr 12 2025 19:00:39
%S A071976 1,2,6,20,70,252,924,3432,12870,48619,184735,705222,2702609,10390940,
%T A071976 40062132,154830696,599641425,2326640877,9042327525,35194002709,
%U A071976 137160956815,535193552973,2090558951396,8174176541450,31990402045260,125301956523471,491168514123342
%N A071976 Number of lists of length n from {0..9} summing to n but not beginning with 0.
%C A071976 Number of n-digit numbers with digit sum n.
%C A071976 Middle diagonal of A213651. - _Miquel Cerda_, Aug 11 2017
%H A071976 Robert Israel, <a href="/A071976/b071976.txt">Table of n, a(n) for n = 1..1100</a>
%H A071976 Ji Young Choi, <a href="https://www.emis.de/journals/JIS/VOL22/Choi/choi15.html">Digit Sums Generalizing Binomial Coefficients</a>, J. Int. Seq., Vol. 22 (2019), Article 19.8.3.
%F A071976 Equals binomial(2n-2, n-1) for n <= 9, by the stars and bars argument. [To get such a number take n boxes in which the leftmost box contains a 1 and the rest are empty. Distribute the remaining n-1 1's into the n boxes subject to the constraint that no box contains more than 9 1's. This can be done in binomial(2n-2, n-1) ways for n <= 9.]
%F A071976 Coefficient of x^n in T^n - T^(n-1), where T = 1+x+...+x^9. - _Robert Israel_, Apr 06 2016
%e A071976 a(3) = 6 as there are six three-digit numbers with digit sum 3: 102, 111, 120, 201, 210, 300.
%e A071976 a(10) = binomial(18,9)-1; a(11) = binomial(20,10)-21; a(12) = binomial(22,11)-210.
%p A071976 T:= add(x^i,i=0..9):
%p A071976 seq(coeff(T^n - T^(n-1),x,n), n=1..25); # _Robert Israel_, Apr 06 2016
%t A071976 Do[c = 0; k = 10^n; l = 10^(n + 1) - 1; While[k < l, If[ Plus @@ IntegerDigits[k] == n + 1, c++ ]; k++ ]; Print[c], {n, 0, 7}]
%o A071976 (PARI) a(n)=local(y=(x^10-1)/(x-1)); if(n<1,0,polcoeff((y-1)*y^(n-1),n))
%Y A071976 Different from A000984.
%Y A071976 Number of n-digit entries in A061384.
%K A071976 nonn,base
%O A071976 1,2
%A A071976 _Amarnath Murthy_, Jun 18 2002
%E A071976 Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, Jun 20 2002
%E A071976 More terms from _Vladeta Jovovic_, Jun 21 2002
%E A071976 More terms from _John W. Layman_, Jun 22 2002