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A352066
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-1,4*k) * a(k).
5
1, 1, 1, 1, 1, 2, 6, 16, 36, 72, 136, 256, 496, 992, 2016, 4096, 8256, 16512, 32896, 65536, 130816, 261633, 523797, 1048807, 2099947, 4206983, 8443911, 17009071, 34452991, 70311167, 144818751, 301455871, 634774911, 1352698367, 2917079551, 6362776831, 14025038591
OFFSET
0,6
LINKS
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x * A(x^4/(1 - x)^4) / (1 - x).
E.g.f.: Integral exp(x) * Sum_{n>=0} a(n) * x^(4*n) / (4*n)! dx.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 4 k] a[k], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 36}]
nmax = 36; A[_] = 0; Do[A[x_] = 1 + x A[x^4/(1 - x)^4]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 02 2022
STATUS
approved