cp's OEIS Frontend

A261741 Number of partitions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order.

%I A261741 #11 May 10 2021 06:24:30
%S A261741 1,7,77,623,5355,40299,317905,2323483,17353028,124991685,907465307,
%T A261741 6458846989,46199021001,326573565143,2314422214435,16296707707077,
%U A261741 114891467946017,806991845455033,5672334432498356,39785054428093380,279156880971492454,1956352659297436368
%N A261741 Number of partitions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order.
%H A261741 Alois P. Heinz, <a href="/A261741/b261741.txt">Table of n, a(n) for n = 0..1000</a>
%F A261741 a(n) ~ c * 7^n, where c = Product_{k>=2} 1/(1 - binomial(k+6,6)/7^k) = 3.519268129363442517546929108933080435102442778133731795486515352... - _Vaclav Kotesovec_, Oct 11 2017, updated May 10 2021
%F A261741 G.f.: Product_{k>=1} 1 / (1 - binomial(k+6,6)*x^k). - _Ilya Gutkovskiy_, May 10 2021
%p A261741 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A261741       b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+6, 6))))
%p A261741     end:
%p A261741 a:= n-> b(n$2):
%p A261741 seq(a(n), n=0..30);
%Y A261741 Column k=7 of A261718.
%K A261741 nonn
%O A261741 0,2
%A A261741 _Alois P. Heinz_, Aug 30 2015