A276367 G.f.: A(x) = Sum_{n>=1} Product_{k=0..n-1} (x + k*A(x)).

1, 2, 8, 46, 322, 2564, 22482, 213358, 2170856, 23563266, 272229894, 3345403228, 43736868406, 608546129090, 9012054592672, 141977836757366, 2376612322575818, 42191783298374292, 792519258202255050, 15709695283993859430, 327743321824492243272, 7177487348025844367658, 164595689482728908058190, 3943617273778939651118764, 98517855256524601996722238, 2561403841975017528679295466, 69192589389178960801205055872

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..125 (terms 1..100 from Paul D. Hanna)

Formula

G.f.: A(x) = Sum_{n>=1} Sum_{k=1..n} |S1(n,k)| * x^k * A(x)^(n-k), where |S1(n,k)| = A000254(n,k) form the unsigned Stirling numbers of first kind.

Example

G.f.: A(x) = x + 2*x^2 + 8*x^3 + 46*x^4 + 322*x^5 + 2564*x^6 + 22482*x^7 + 213358*x^8 + 2170856*x^9 + 23563266*x^10 + 272229894*x^11 + 3345403228*x^12 + 43736868406*x^13 + 608546129090*x^14 + 9012054592672*x^15 + 141977836757366*x^16 +...
such that
A(x) = x + x*(x + A(x)) + x*(x + A(x))*(x + 2*A(x)) + x*(x + A(x))*(x + 2*A(x))*(x + 3*A(x)) + x*(x + A(x))*(x + 2*A(x))*(x + 3*A(x))*(x + 4*A(x)) + x*(x + A(x))*(x + 2*A(x))*(x + 3*A(x))*(x + 4*A(x))*(x + 5*A(x)) +...

Prog

(PARI) {a(n) = my(A=x); for(i=1, n, A = sum(m=1, 30, prod(k=0, m-1, x + k*A +x*O(x^n)))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
(PARI) {a(n) = my(A=x); for(i=0, n, A = sum(m=1, n, sum(k=1, m, abs( stirling(m, k, 1) )*x^k*(A + x*O(x^n))^(m-k) ) ) ); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A258315 A334498 A006664 * A326351 A276358 A337060

Adjacent sequences: A276364 A276365 A276366 * A276368 A276369 A276370

Keyword

nonn

Author

Paul D. Hanna, Sep 02 2016

Status

approved