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 A353180 Expansion of e.g.f. 1/(1 - Sum_{k>=1} x^(k^2) / (k^2)!). 2
 1, 1, 2, 6, 25, 130, 810, 5880, 48790, 455491, 4725020, 53915730, 671141130, 9050528630, 131437406100, 2045160117000, 33944105995801, 598591246152934, 11176863039391538, 220287874849834596, 4570225746232479690, 99557506547622369750, 2272028399094852806100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..22. FORMULA a(0) = 1; a(n) = Sum_{k=1..floor(sqrt(n))} binomial(n,k^2) * a(n-k^2). MATHEMATICA a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k^2] * a[n - k^2], {k, 1, Floor@Sqrt[n]}]; Array[a, 23, 0] (* Amiram Eldar, Apr 30 2022 *) PROG (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, sqrtint(N), x^k^2/(k^2)!)))) (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, sqrtint(i), binomial(i, j^2)*v[i-j^2+1])); v; CROSSREFS Cf. A006456, A205802, A329256, A353184. Sequence in context: A030933 A299044 A100325 * A352428 A352436 A020112 Adjacent sequences: A353177 A353178 A353179 * A353181 A353182 A353183 KEYWORD nonn AUTHOR Seiichi Manyama, Apr 29 2022 STATUS approved

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Last modified February 29 13:01 EST 2024. Contains 370425 sequences. (Running on oeis4.)