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A208886 G.f.: Sum_{n>=0} (2*n+1)! * x^n / Product_{k=1..2*n+1} (1 + k*x). 2
1, 5, 85, 3389, 238021, 25791485, 3982831525, 830287473629, 224589628828741, 76476839514843965, 32008234421462900965, 16149704161940128467869, 9666556369631455442262661, 6772084092710344017948232445, 5489289305870251277606850778405 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1+k*x).
LINKS
FORMULA
a(n) ~ sqrt(Pi) * 2^(2*n+2) * n^(2*n+3/2) / exp(2*n+1/2). - Vaclav Kotesovec, Nov 01 2014
EXAMPLE
G.f.: A(x) = 1 + 5*x + 85*x^2 + 3389*x^3 + 238021*x^4 + 25791485*x^5 +...
such that
A(x) = 1/(1+x) + 3!*x/((1+x)*(1+2*x)*(1+3*x)) + 5!*x^2/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)) + 7!*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)*(1+7*x)) + 9!*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)*(1+6*x)*(1+7*x)*(1+8*x)*(1+9*x)) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, (2*m+1)!*x^m/prod(k=1, 2*m+1, 1+k*x+x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A277354 A101928 A012788 * A192055 A012815 A113107
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 04 2012
STATUS
approved

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Last modified February 21 16:55 EST 2024. Contains 370237 sequences. (Running on oeis4.)