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A303652 Column sums of irregular triangle A303650. 2
1, 4, 23, 269, 6080, 263107, 21755790, 3448734174, 1054337703035, 625864795912552, 726009710371573669, 1654701176883966564948, 7441600457415936633083792, 66248198041546539808288183964, 1170186904620869164091169463554964, 41080483613395453869669149072267922983 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

G.f.: (1-x)^2 * Sum_{n>=0} (2*n+1) * x^n * (1 + (1-x)^2)^(n*(n+1)/2).

EXAMPLE

G.f.: A(x) = 1 + 4*x + 23*x^2 + 269*x^3 + 6080*x^4 + 263107*x^5 + 21755790*x^6 + 3448734174*x^7 + 1054337703035*x^8 + ...

such that

A(x)/(1-x)^2 = 1 + 3*x*(2-2*x+x^2) + 5*x^2*(2-2*x+x^2)^3 + 7*x^3*(2-2*x+x^2)^6 + 9*x^4*(2-2*x+x^2)^10 + 11*x^5*(2-2*x+x^2)^15 + 13*x^6*(2-2*x+x^2)^21 +...

PROG

(PARI) {a(n) = my(A = (1-x)^2 * sum(m=0, n, (2*m+1) * x^m * (1 + (1-x)^2 +x*O(x^n) )^(m*(m+1)/2) ) ); polcoeff(A, n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A303650, A303651.

Sequence in context: A293510 A234595 A327367 * A130890 A138578 A219932

Adjacent sequences:  A303649 A303650 A303651 * A303653 A303654 A303655

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 30 2018

STATUS

approved

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Last modified November 17 16:08 EST 2019. Contains 329241 sequences. (Running on oeis4.)