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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
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
Sequence in context: A030933 A299044 A100325 * A352428 A352436 A020112
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.)