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 A365898 Expansion of e.g.f. exp( Sum_{k>=0} x^(4*k+5) / (4*k+5)! ). 4

%I #15 Sep 23 2023 07:26:16

%S 1,0,0,0,0,1,0,0,0,1,126,0,0,1,2002,126126,0,1,32878,11639628,

%T 488864376,1,523754,962159506,164910249504,5194672859377,8390630,

%U 79198593760,44919303188760,4895979169961881,123378675217248882,6434084214390,11762691848427520

%N Expansion of e.g.f. exp( Sum_{k>=0} x^(4*k+5) / (4*k+5)! ).

%H Seiichi Manyama, <a href="/A365898/b365898.txt">Table of n, a(n) for n = 0..609</a>

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/4)} binomial(n-1,4*k+4) * a(n-4*k-5).

%F E.g.f.: exp( -x + (sinh(x) + sin(x))/2 ).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\4, x^(4*k+5)/(4*k+5)!))))

%Y Cf. A057814, A365896, A365897.

%K nonn

%O 0,11

%A _Seiichi Manyama_, Sep 22 2023

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Last modified July 24 12:16 EDT 2024. Contains 374583 sequences. (Running on oeis4.)