A381347 Expansion of e.g.f. 1/( 1 - sin(sqrt(2)*x) / sqrt(2) ).
1, 1, 2, 4, 8, 4, -112, -1184, -9088, -59504, -310528, -643136, 14701568, 323581504, 4554426368, 51666451456, 458243735552, 2004840714496, -37024075153408, -1386061762251776, -29290212127670272, -483475390212586496, -6224109737622372352, -45231727252157947904
Offset: 0
Keywords
Programs
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PARI
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j)); a(n) = sum(k=0, n, k!*(-2)^((n-k)/2)*a136630(n, k));
Formula
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * binomial(n,2*k+1) * a(n-2*k-1).
a(n) = Sum_{k=0..n} k! * (-2)^((n-k)/2) * A136630(n,k)