cp's OEIS Frontend

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.

A336997 a(n) = n! * Sum_{d|n} 2^(d - 1) / d!.

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%I A336997 #8 Aug 12 2020 11:10:18
%S A336997 1,4,10,56,136,1952,5104,94208,605056,7741952,39917824,1458295808,
%T A336997 6227024896,175463616512,2353813878784,48886264659968,355687428161536,
%U A336997 17362063156969472,121645100409094144,6001501553433509888,85800344155030552576,2248030289949388439552
%N A336997 a(n) = n! * Sum_{d|n} 2^(d - 1) / d!.
%F A336997 E.g.f.: Sum_{k>=1} (exp(2*x^k) - 1) / 2.
%F A336997 a(p) = p! + 2^(p - 1), where p is prime.
%t A336997 Table[n! Sum[2^(d - 1)/d!, {d, Divisors[n]}], {n, 1, 22}]
%t A336997 nmax = 22; CoefficientList[Series[Sum[(Exp[2 x^k] - 1)/2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%o A336997 (PARI) a(n) = n! * sumdiv(n, d, 2^(d-1)/d!); \\ _Michel Marcus_, Aug 12 2020
%Y A336997 Cf. A010842, A034729, A057625, A336998.
%K A336997 nonn
%O A336997 1,2
%A A336997 _Ilya Gutkovskiy_, Aug 10 2020