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 A227467 E.g.f.: exp( Sum_{n>=1} (1+x)^(n^2) * x^n/n ). 2
 1, 1, 4, 24, 252, 3660, 73560, 1921080, 63411600, 2574406800, 125747475840, 7258472907840, 487590023511360, 37629962101892160, 3299990581104497280, 325758967714868688000, 35904380354917794720000, 4387164775718671231084800, 590610815931660911894707200, 87118296156852814044256665600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare the definition to: exp( Sum_{n>=1} (1+y)^(n^2) * x^n/n ), which yields an integer series whenever y is an integer. Note that exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, n*k) * x^k ) yields an integer series (A206830). LINKS EXAMPLE E.g.f.: A(x) = 1 + x + 4*x^2/2! + 24*x^3/3! + 252*x^4/4! + 3660*x^5/5! +... where, by definition, log(A(x)) = (1+x)*x + (1+x)^4*x^2/2 + (1+x)^9*x^3/3 + (1+x)^16*x^4/4 + (1+x)^25*x^5/5+ (1+x)^36*x^6/6+ (1+x)^49*x^7/7 +... PROG (PARI) {a(n)=n!*polcoeff(exp(sum(m=1, n, (1+x)^(m^2)*x^m/m)+x*O(x^n)), n)} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A206830, A167006. Sequence in context: A325963 A141013 A330469 * A176785 A318000 A095340 Adjacent sequences:  A227464 A227465 A227466 * A227468 A227469 A227470 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 24 2013 STATUS approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)